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## Solonnikov, Vsevolod Alekseevich

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 Author ID: solonnikov.vsevolod-alekseevich Published as: Solonnikov, V. A.; Solonnikov, Vsevolod A.; Solonnikov, Vsevolod Alekseevich; Solonnikov, Vsevolod; Solonnikov, V.; Solonnikov, Vsevolod Alekseevič External Links: MGP · Wikidata · Math-Net.Ru · GND
 Documents Indexed: 332 Publications since 1958, including 14 Books Biographic References: 6 Publications
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#### Co-Authors

 184 single-authored 18 Ladyzhenskaya, Ol’ga Aleksandrovna 10 Denisova, Irina Vlad. 9 Frolova, E. V. 9 Garroni, Maria Giovanna 9 Vivaldi, Maria Agostina 8 Maremonti, Paolo 7 Golovkin, Kirill Kapitonovich 7 Grubb, Gerd 7 Padula, Mariarosaria 6 Pileckas, Konstantin 6 Ural’tseva, Nina Nikolaevna 5 Rautmann, Reimund 5 Tani, Atusi 4 Birman, Mikhail Shlëmovich 4 Bizhanova, Galina I. 4 Fasano, Antonio 4 Hildebrandt, Stefan 4 Khachatryan, A. G. 4 Mogilevskii, Ilya Shulimovich 4 Mulone, Giuseppe 3 Heywood, John G. 3 Il’in, Valentin Petrovich 3 Masuda, Kyûya 3 Yi, Fahuai 2 Galdi, Giovanni Paolo 2 Mosconi, Sunra J. N. 2 Rivkind, L. P. 2 Rokhman, I. M. 2 Vasil’ev, V. N. 2 Zajączkowski, Wojciech M. 1 Amann, Herbert 1 Antontsev, Stanislav Nikolaevich 1 Clarotti, C. A. 1 Finn, Robert S. 1 Hansen, Erik B. 1 Kazhikov, Aleksandr Vasil’evich 1 Koch, Herbert 1 Kokh, Kh. 1 Meirmanov, Anvarbek Mukatovich 1 Novotný, Antonín 1 Panich, O. I. 1 Penel, Patrick 1 Pukhnachov, Vladislav Vasil’evich 1 Rădulescu, Vicenţiu D. 1 Rodrigues, José Francisco 1 Sahaev, Sh. 1 Sahaev, Sh. 1 Sakhaev, Sharipkhan 1 Scadilov, V. E. 1 Sequeira, Adélia 1 Seregin, Gregory A. 1 Shilkin, T. N. 1 Spizzichino, Fabio L. 1 True, Hans
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#### Fields

 274 Partial differential equations (35-XX) 191 Fluid mechanics (76-XX) 15 Functional analysis (46-XX) 12 Operator theory (47-XX) 10 General and overarching topics; collections (00-XX) 7 Classical thermodynamics, heat transfer (80-XX) 5 Integral equations (45-XX) 4 Potential theory (31-XX) 4 Ordinary differential equations (34-XX) 4 Numerical analysis (65-XX) 3 Mechanics of deformable solids (74-XX) 3 Astronomy and astrophysics (85-XX) 2 Real functions (26-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Probability theory and stochastic processes (60-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

248 Publications have been cited 3,263 times in 2,217 Documents Cited by Year
Linear and quasi-linear equations of parabolic type. Translated from the Russian by S. Smith. Zbl 0174.15403
Ladyzhenskaya, O. A.; Solonnikov, V. A.; Ural’tseva, N. N.
1968
Linear and quasilinear equations of parabolic type. (Линейные и квазилинейные уравнения параболического типа.) Zbl 0164.12302
Ladyzhenskaya, O. A.; Solonnikov, V. A.; Ural’tseva, N. N.
1967
Estimates for solutions of nonstationary Navier-Stokes equations. Zbl 0404.35081
Solonnikov, V. A.
1977
On boundary value problems for linear parabolic systems of differential equations of general form. Zbl 0164.12502
Solonnikov, V. A.
1965
On a boundary value problem for a stationary system of Navier-Stokes equations. Zbl 0313.35063
Solonnikov, V. A.; Scadilov, V. E.
1973
Unique solvability of an initial- and boundary-value problem for viscous incompressible nonhomogeneous fluids. Zbl 0401.76037
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1978
On some problems of vector analysis and generalized formulations of boundary-value problems for the Navier-Stokes equations. Zbl 0346.35084
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1976
Boundary value problems for the nonstationary Navier-Stokes equations treated by pseudo-differential methods. Zbl 0766.35034
Grubb, Gerd; Solonnikov, Vsevolod A.
1991
Abschätzungen der Lösungen eines instationären Navier-Stokesschen Systems. Zbl 0346.35083
Solonnikov, V. A.
1973
A-priori-Abschätzungen für Gleichungen zweiter Ordnung vom parabolischen Typ. Zbl 0168.08202
Solonnikov, V. A.
1964
Some problems of vector analysis and generalized formulations of boundary-value problems for the Navier-Stokes equations. Zbl 0388.35061
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1978
On nonstationary Stokes problem and Navier-Stokes problem in a half-space with initial data nondecreasing at infinity. Zbl 1054.35059
Solonnikov, V. A.
2003
Abschätzung der Lösung des nichtstationären linearisierten Navier- Stokesschen Gleichungssystems. Zbl 0163.33803
Solonnikov, V. A.
1964
On nonstationary Stokes problem in exterior domains. Zbl 0958.35103
Maremonti, P.; Solonnikov, V. A.
1997
On the unique solvability of the initial value problem for viscous incompressible inhomogeneous fluids. Zbl 0376.76021
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1975
Solvability of a problem on the motion of a viscous incompressible fluid bounded by a free surface. Zbl 0398.76024
Solonnikov, V. A.
1977
Estimates for solutions of the nonstationary Stokes problem in anisotropic Sobolev spaces and estimates for the resolvent of the Stokes operator. Zbl 1059.35101
Solonnikov, V. A.
2003
Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations. Zbl 0187.03402
Solonnikov, V. A.
1968
Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid. Zbl 0451.35092
Solonnikov, V. A.
1980
On the solvability of the initial-boundary problem for the equation of motion of the viscous compressible fluid. Zbl 0338.35078
Solonnikov, V. A.
1976
On the solvability of boundary and initial-boundary value problems for the Navier-Stokes system in domains with noncompact boundaries. Zbl 0413.35062
Solonnikov, V. A.
1981
The linearization principle and invariant manifolds for problems of magnetohydrodynamics. Zbl 0404.35089
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1977
On finding solutions of boundary value problems for stationary Stokes and Navier-Stokes equations which have an unbounded Dirichlet integral. Zbl 0463.35069
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1980
Estimates of solutions of the Stokes equations in S. L. Sobolev spaces with a mixed norm. Zbl 1068.35093
Solonnikov, V. A.
2002
Determination of the solutions of boundary value problems for stationary Stokes and Navier-Stokes equations having an unbounded Dirichlet integral. Zbl 0509.35066
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1983
On the transient motion of an isolated volume of viscous incompressible fluid. Zbl 0850.76180
Solonnikov, V. A.
1987
Existence theorems for the equations of motion of a compressible viscous fluid. Zbl 0492.76074
Solonnikov, V. A.; Kazhikhov, A. V.
1981
Solvability of the problem on evolution of a viscous incompressible fluid bounded by a free surface on a finite time interval. Zbl 0850.76132
Solonnikov, V. A.
1991
Free boundary problem for a viscous compressible flow with a surface tension. Zbl 0752.35096
Solonnikov, V. A.; Tani, A.
1991
On the solvability of boundary and initial-boundary value problems for Navier-Stokes equations in domains with non-compact boundaries. Zbl 0377.35060
Ladyzhenskaya, O. A.; Solonnikov, V. A.
1977
Solvability of a three-dimensional problem with a free boundary for the stationary system of Navier-Stokes equations. Zbl 0414.35062
Solonnikov, V. A.
1979
Über allgemeine Randwertprobleme für Systeme, die im Sinne von A. Douglis - L. Nirenberg elliptisch sind. I. Zbl 0128.33003
Solonnikov, V. A.
1964
Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid. Zbl 0786.35106
Solonnikov, V. A.; Tani, A.
1992
Abschätzungen der Lösung für das Anfangs-Randwertproblem für ein lineares instationäres System von Navier-Stokesschen Gleichungen. Zbl 0357.76026
Solonnikov, V. A.
1976
Solvability of the problem concerning the evolution of an isolated volume of viscous incompressible capillary liquid. Zbl 0551.76022
Solonnikov, V. A.
1984
A priori estimates for second-order parabolic equations. Zbl 0179.42901
Solonnikov, V. A.
1967
General boundary value problems for Douglis-Nirenberg elliptic systems. Zbl 0168.36701
Solonnikov, V. A.
1966
Lectures on evolution free boundary problems: classical solutions. Zbl 1038.35063
Solonnikov, Vsevolod A.
2003
Boundary partial regularity for the Navier-Stokes equations. Zbl 1095.35031
Seregin, G. A.; Shilkin, T. N.; Solonnikov, V. A.
2004
Unsteady motion of a finite mass of fluid, bounded by a free surface. Zbl 0639.76035
Solonnikov, V. A.
1988
On the solvability of classical initial-boundary value problems for the heat equation in a dihedron. Zbl 0557.35064
Solonnikov, V. A.
1984
Über Differentialeigenschaften der Lösung des ersten Randwertproblems für das nichtstationäre System der Navier-Stokesschen Gleichungen. Zbl 0163.33901
Solonnikov, V. A.
1964
Estimates for solutions of the nonstationary Stokes problem in anisotropic Sobolev spaces with mixed norm. Zbl 0909.35105
Maremonti, P.; Solonnikov, V. A.
1995
On estimates of Green’s tensors for certain boundary problems. Zbl 0097.30404
Solonnikov, V.
1960
On general boundary problems for systems which are elliptic in the sense of A. Douglis and L. Nirenberg. I. Zbl 0175.11703
Solonnikov, V. A.
1964
$$L_ p$$-estimates for solutions of the heat equation in a dihedral angle. Zbl 1052.35046
Solonnikov, V. A.
2001
Solution of parabolic pseudo-differential initial-boundary value problems. Zbl 0713.35109
Grubb, Gerd; Solonnikov, Vsevolod A.
1990
Nonstationary motion of a finite isolated mass in a self-gravitating fluid. Zbl 0713.76044
Solonnikov, V. A.
1989
Schauder estimates for the evolutionary generalized Stokes problem. Zbl 1361.35135
Solonnikov, V. A.
2007
On the local solvability of free boundary problem for the Navier-Stokes equations. Zbl 1357.35247
Padula, M.; Solonnikov, V. A.
2010
On a parabolic system with time derivative in the boundary conditions and related free boundary problems. Zbl 0940.35211
Rodrigues, J. F.; Solonnikov, V. A.; Yi, F.
1999
Weighted Schauder estimates for evolution Stokes problem. Zbl 1115.35105
Solonnikov, Vsevolod A.
2006
Unsteady flow of a finite mass of a liquid bounded by a free surface. Zbl 0614.76026
Solonnikov, V. A.
1986
Free boundary problems for second order parabolic equations. Zbl 0997.35102
Bizhanova, G. I.; Solonnikov, V. A.
2001
On the Neumann problem for second order elliptic equations in domains with edges at the boundary. Zbl 0518.35030
Zajaczkowski, W.; Solonnikov, V. A.
1983
On an initial-boundary value problem for the Stokes systems arising in the study of a problem with a free boundary. Zbl 0731.35079
Solonnikov, V. A.
1991
On overdetermined elliptic boundary value problems. Zbl 0231.35029
Solonnikov, V. A.
1971
$$L_p$$-theory for the Stefan problem. Zbl 0906.35119
Solonnikov, V. A.; Frolova, E. V.
1997
Solvability of an initial-boundary value problem with time derivative in the boundary condition for a second order parabolic equation in a weighted Hölder function space. Zbl 0805.35043
Bizhanova, G. I.; Solonnikov, V. A.
1993
On some free boundary problems for the Navier-Stokes equations with moving contact points and lines. Zbl 0926.35116
Solonnikov, V. A.
1995
On the justification of the quasistationary approximation in the problem of motion of a viscous capillary drop. Zbl 0974.35097
Solonnikov, V. A.
1999
Estimates for the solution of the second initial boundary-value problem for the Stokes system in the spaces of functions having Hölder continuous derivatives with respect to the spatial variables. Zbl 1153.76349
Solonnikov, V. A.
1999
On the problem of dynamic contact angle. Zbl 0532.76026
Pukhnachev, V. V.; Solonnikov, V. A.
1983
Classical solvability of the problem on the motion of two viscous incompressible fluids. Zbl 0859.35093
Denisova, I. V.; Solonnikov, V. A.
1995
On the solvability of the second initial-boundary value problem for the linear non-stationary Navier-Stokes system. Zbl 0348.35079
Solonnikov, V. A.
1977
Estimates of the solutions of initial boundary value problems in weighted Hölder norms. Zbl 0442.35016
Solonnikov, V. A.; Khachatryan, A. G.
1980
On the global existence of nonsteady motions of a fluid drop and their exponential decay to a uniform rigid rotation. Zbl 1284.76095
Padula, M.; Solonnikov, V. A.
2002
On parabolic oblique derivative problem with Hölder continuous coefficients. Zbl 0562.35044
Garroni, M. G.; Solonnikov, V. A.
1984
Certain spaces of solenoidal vectors and the solvability of the boundary problem for the Navier-Stokes system of equations in domains with noncompact boundaries. Zbl 0612.35111
Solonnikov, V. A.; Piletskas, K. I.
1986
On quasistationary approximation in the problem of motion of a capillary drop. Zbl 0919.35103
Solonnikov, V. A.
1999
Green’s matrices for elliptic boundary value problems. II. Zbl 0231.35030
Solonnikov, V. A.
1971
On an initial-boundary value problem for the equation of magnetohydrodynamics with the Hall and ion-slip effects. Zbl 0927.76100
Mulone, G.; Solonnikov, V. A.
1995
Existence, uniqueness and asymptotic behaviour of solutions of steady-state Navier-Stokes equations in a plane aperture domain. Zbl 0990.35116
Galdi, G. P.; Padula, M.; Solonnikov, V. A.
1996
The solvability of the second initial boundary-value problem for the linear, time-dependent system of Navier-Stokes equations. Zbl 0388.35059
Solonnikov, V. A.
1978
$$L_q$$-estimates of the first-order derivatives of solutions to the nonstationary Stokes problem. Zbl 1046.35085
Koch, Herbert; Solonnikov, Vsevolod A.
2002
Global solvability of a problem governing the motion of two incompressible capillary fluids in a container. Zbl 1278.35175
Denisova, I. V.; Solonnikov, V. A.
2012
Solvability of the classical initial-boundary-value problems for the heat-conduction equation in a dihedral angle. Zbl 0582.35055
Solonnikov, V. A.
1986
On Green’s matrices for elliptic boundary value problems. I. Zbl 0244.35042
Solonnikov, V. A.
1972
Overdetermined elliptic boundary-value problems. Zbl 0285.35026
Solonnikov, V. A.
1973
On a problem of magnetohydrodynamics in a multi-connected domain. Zbl 1402.35227
Mosconi, Sunra J. N.; Solonnikov, Vsevolod A.
2011
On the free boundary problem of magnetohydrodynamics. Zbl 1304.35782
Padula, M.; Solonnikov, V. A.
2011
On problems of the hydrodynamics of a viscous incompressible fluid in domains with noncompact boundaries. Zbl 0840.35078
Solonnikov, V. A.
1992
On the solvability of an evolution free boundary problem for the Navier-Stokes equations in Hölder spaces of functions. Zbl 0793.35072
Mogilevskij, I. S.; Solonnikov, V. A.
1992
On the stability of nonsymmetric equilibrium figures of a rotating viscous incompressible liquid. Zbl 1068.35114
Solonnikov, V. A.
2004
Estimates of solutions of an initial- and boundary-value problem for the linear nonstationary Navier-Stokes system. Zbl 0389.76024
Solonnikov, V. A.
1978
Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container. Zbl 0429.76020
Solonnikov, V. A.
1980
Estimate of the generalized energy in a free-boundary problem for a viscous incompressible fluid. Zbl 1075.35041
Solonnikov, V. A.
2001
Solvability of the linearized problem on the motion of a drop in a liquid flow. Zbl 0796.76025
Denisova, I. V.; Solonnikov, V. A.
1989
Solvability of three-dimensional problems with a free boundary for a stationary system of Navier-Stokes equations. Zbl 0515.35073
Solonnikov, V. A.
1983
On a problem with a third boundary condition for the Laplace equation in a plane angle and its application to parabolic problems. Zbl 0711.35036
Solonnikov, V. A.; Frolova, E. V.
1990
Classical solvability of a model problem in a half-space, related to the motion of an isolated mass of a compressible fluid. Zbl 1118.76312
Denisova, I. V.; Solonnikov, V. A.
2000
An estimate for the solutions of Stokes equations in exterior domains. Zbl 0792.35130
Maremonti, P.; Solonnikov, V. A.
1990
On some spaces of divergence-free vector fields and on the solvability of a boundary-value problem for Navier-Stokes equations in domains with non- compact boundaries. Zbl 0406.35054
Solonnikov, V. A.; Piletskas, K. I.
1977
On instability of axially symmetric equilibrium figures of rotating viscous incompressible liquid. Zbl 1075.35042
Solonnikov, V. A.
2004
Solvability in Hölder spaces for a model initial-boundary value problem generated by a problem on the motion of two fluids. Zbl 0756.35067
Denisova, I. V.; Solonnikov, V. A.
1991
Estimates in $$L_ p$$ of solutions of elliptic and parabolic systems. Zbl 0204.42101
Solonnikov, V. A.
1969
Estimates of convolution operators. Zbl 0205.14602
Golovkin, K. K.; Solonnikov, V. A.
1968
Abschätzungen von Integraloperatoren in translationsinvarianten Normen. Zbl 0163.33204
Golovkin, K. K.; Solonnikov, V. A.
1964
On the oblique derivative problem in an infinite angle. Zbl 0897.35023
Garroni, M. G.; Solonnikov, V. A.; Vivaldi, M. A.
1996
Boundary and initial-boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries. Zbl 0794.76025
Solonnikov, V. A.
1993
On the model problem arising in the study of motion of viscous compressible and incompressible fluids with a free interface. Zbl 1414.35151
Solonnikov, V. A.
2019
$$L_2$$-theory for two incompressible fluids separated by a free interface. Zbl 1416.35182
Denisova, Irina V.; Solonnikov, Vsevolod A.
2018
On the solvability of free boundary problem for viscous compressible fluids in an infinite time interval. Zbl 1371.35224
Solonnikov, Vsevolod Alekseevich
2016
On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations. Zbl 1323.45003
Sahaev, Sh.; Solonnikov, V. A.
2015
$$L_p$$-theory of the problem of motion of two incompressible capillary fluids in a container. Zbl 1309.35093
Solonnikov, V. A.
2014
Viscous incompressible free-surface flow down an inclined perturbed plane. Zbl 1302.35298
Pileckas, K.; Solonnikov, V. A.
2014
$$L_p$$-theory of free boundary problems of magnetohydrodynamics in simply connected domains. Zbl 1328.35335
Solonnikov, V. A.
2014
Solvability of a free boundary problem of magnetohydrodynamics in an infinite time interval. Zbl 1308.76338
Solonnikov, V. A.; Frolova, E. V.
2013
$$L_p$$-estimates for a linear problem arising in the study of the motion of an isolated liquid mass. Zbl 1283.35068
Solonnikov, V. A.
2013
Mixed type, nonlinear systems in polygonal domains. Zbl 1276.35118
Solonnikov, Vsevolod A.; Vivaldi, Maria A.
2013
Global solvability of a problem governing the motion of two incompressible capillary fluids in a container. Zbl 1278.35175
Denisova, I. V.; Solonnikov, V. A.
2012
On some stationary problems of magnetohydrodynamics in multi-connected domains. Zbl 1261.35123
Sakhaev, Sh.; Solonnikov, V. A.
2012
Free boundary problems of magnetohydrodynamics in multi-connected domains. Zbl 1282.35315
Solonnikov, Vsevolod A.
2012
On the stability of uniformly rotating viscous incompressible self-gravitating liquid. Zbl 1287.35109
Solonnikov, Vsevolod A.
2012
$$L_{p}$$-estimates of the solution of a linear problem arising in magnetohydrodynamics. Zbl 1234.35202
Solonnikov, V.
2012
On a problem of magnetohydrodynamics in a multi-connected domain. Zbl 1402.35227
Mosconi, Sunra J. N.; Solonnikov, Vsevolod A.
2011
On the free boundary problem of magnetohydrodynamics. Zbl 1304.35782
Padula, M.; Solonnikov, V. A.
2011
On the linear problem arising in the study of a free boundary problem for the Navier-Stokes equations. Zbl 1230.35090
Solonnikov, V. A.
2011
On the stability of uniformly rotating liquid in a weak magnetic field. Zbl 1290.76163
Solonnikov, V. A.
2011
On the local solvability of free boundary problem for the Navier-Stokes equations. Zbl 1357.35247
Padula, M.; Solonnikov, V. A.
2010
Linearization principle for a system of equations of mixed type. Zbl 1178.35061
Mulone, G.; Solonnikov, V. A.
2009
Schauder estimates for a system of equations of mixed type. Zbl 1183.35209
Garroni, M. G.; Solonnikov, V. A.; Vivaldi, M. A.
2009
On the nonstationary motion of a viscous incompressible liquid over a rotating ball. Zbl 1214.35087
Solonnikov, V. A.
2009
A simple proof of the linear instability of rotating liquid drops. Zbl 1248.76059
Padula, Mariarosaria; Solonnikov, Vsevolod A.
2008
On estimates for volume and surface potentials in domains with boundary of class $$W_{2}^{l}$$. Zbl 1202.31005
Solonnikov, V. A.
2008
On estimates for potentials related to the problem of stability of a rotating self-gravitating liquid. Zbl 1202.35360
Solonnikov, V. A.
2008
Schauder estimates for the evolutionary generalized Stokes problem. Zbl 1361.35135
Solonnikov, V. A.
2007
On the linear problem related to the stability of uniformly rotating self-gravitating liquid. Zbl 1202.35178
Solonnikov, V. A.
2007
On Schauder estimates for the evolution generalized Stokes problem. Zbl 1123.35005
Solonnikov, Vsevolod A.
2007
On stability of equilibrium figures of a uniformly rotating liquid drop in $$n$$-dimensional space. Zbl 1119.35058
Padula, M.; Solonnikov, V. A.
2007
On the problem of non-stationary motion of two viscous incompressible liquids. Zbl 1202.35177
Solonnikov, V. A.
2007
Weighted Schauder estimates for evolution Stokes problem. Zbl 1115.35105
Solonnikov, Vsevolod A.
2006
Estimates of the solution of model evolution generalized Stokes problem in weighted Hölder spaces. Zbl 1127.35051
Solonnikov, V. A.
2006
Letter to the editor: Erratum to: “On a linear problem connected with equilibrium figures of a uniformly rotating viscous liquid”. Zbl 1114.35026
Solonnikov, V. A.
2006
On instability of equilibrium figures of rotating viscous incompressible self-gravitating liquid not subjected to capillary forces. Zbl 1119.35069
Solonnikov, V. A.
2006
Weighted estimates for the solution of a linear problem associated with the one-phase Stefan problem in the case when the specific heat tends to zero. Zbl 1123.35093
Solonnikov, V. A.; Frolova, E. V.
2006
On instability of equilibrium figures of rotating viscous incompressible liquid. Zbl 1099.76022
Solonnikov, V. A.
2005
On the stability of axially symmetric equilibrium figures of a rotating viscous incompressible fluid. Zbl 1068.35092
Solonnikov, V. A.
2005
On linear stability and instability of equilibrium figures of uniformly rotating liquid. Zbl 1140.76335
Solonnikov, V. A.
2005
Boundary partial regularity for the Navier-Stokes equations. Zbl 1095.35031
Seregin, G. A.; Shilkin, T. N.; Solonnikov, V. A.
2004
On the stability of nonsymmetric equilibrium figures of a rotating viscous incompressible liquid. Zbl 1068.35114
Solonnikov, V. A.
2004
On instability of axially symmetric equilibrium figures of rotating viscous incompressible liquid. Zbl 1075.35042
Solonnikov, V. A.
2004
Estimates for the resolvent of the operator appearing in the study of equilibrium figures of a rotating viscous incompressible fluid. Zbl 1099.35105
Solonnikov, V. A.
2004
The problem on evolution of a self-gravitating isolated fluid mass that is not subject to the surface tension forces. Zbl 1099.35182
Solonnikov, V. A.
2004
On nonstationary Stokes problem and Navier-Stokes problem in a half-space with initial data nondecreasing at infinity. Zbl 1054.35059
Solonnikov, V. A.
2003
Estimates for solutions of the nonstationary Stokes problem in anisotropic Sobolev spaces and estimates for the resolvent of the Stokes operator. Zbl 1059.35101
Solonnikov, V. A.
2003
Lectures on evolution free boundary problems: classical solutions. Zbl 1038.35063
Solonnikov, Vsevolod A.
2003
Classical solvability of a problem on the motion of an isolated mass of compressible fluid. Zbl 1037.35103
Denisova, I. V.; Solonnikov, V. A.
2003
$$L_q$$-estimates for a solution to the problem about the evolution of an isolated amount of a fluid. Zbl 1054.35070
Solonnikov, V. A.
2003
Unsaturated incompressible flows in adsorbing porous media. Zbl 1066.76060
Fasano, A.; Solonnikov, V.
2003
On the problem of evolution of an isolated liquid mass. Zbl 1071.76023
Solonnikov, V. A.
2003
Estimates of solutions of the Stokes equations in S. L. Sobolev spaces with a mixed norm. Zbl 1068.35093
Solonnikov, V. A.
2002
On the global existence of nonsteady motions of a fluid drop and their exponential decay to a uniform rigid rotation. Zbl 1284.76095
Padula, M.; Solonnikov, V. A.
2002
$$L_q$$-estimates of the first-order derivatives of solutions to the nonstationary Stokes problem. Zbl 1046.35085
Koch, Herbert; Solonnikov, Vsevolod A.
2002
Existence of non-steady flows of an incompressible, viscous drop of fluid in a frame rotating with finite angular velocity. Zbl 1039.35018
Padula, M.; Solonnikov, V. A.
2002
On the theory of nonstationary hydrodynamic potentials. Zbl 0995.35044
Solonnikov, Vsevolod
2002
Nonlinear problems in mathematical physics and related topics I. In honor of Professor O. A. Ladyzhenskaya. Zbl 0998.00008
Birman, Michael Sh.; Hildebrandt, Stefan; Solonnikov, V. A.; Uraltseva, N. N.
2002
Potential theory for the nonstationary Stokes problem in nonconvex domains. Zbl 1054.35060
Solonnikov, Vsevolod A.
2002
Nonlinear problems in mathematical physics and related topics II. In honour of Professor O. A. Ladyzhenskaya. Zbl 1005.00022
Birman, Michael Sh.; Hildebrandt, Stefan; Solonnikov, Vsevolod A.; Uraltseva, Nina N.
2002
$$L_ p$$-estimates for solutions of the heat equation in a dihedral angle. Zbl 1052.35046
Solonnikov, V. A.
2001
Free boundary problems for second order parabolic equations. Zbl 0997.35102
Bizhanova, G. I.; Solonnikov, V. A.
2001
Estimate of the generalized energy in a free-boundary problem for a viscous incompressible fluid. Zbl 1075.35041
Solonnikov, V. A.
2001
Initial-boundary value problem for generalized Stokes equations. Zbl 0981.35047
Solonnikov, V. A.
2001
$$L_p$$-estimates for a solution to the nonstationary Stokes equations. Zbl 0987.35121
Kokh, Kh.; Solonnikov, V. A.
2001
Smooth interface in a two-component Stokes flow. Zbl 1005.35073
Antontsev, S. N.; Meirmanov, A. M.; Solonnikov, V. A.
2001
$$L_p$$-estimates of solutions of initial-boundary value problem for generalized Stokes equations. Zbl 1003.76016
Solonnikov, V. A.
2001
The exponential behaviour of the Green function in a dihedral angle. Zbl 1075.35524
Garroni, M. G.; Solonnikov, V. A.; Vivaldi, M. A.
2001
Classical solvability of a model problem in a half-space, related to the motion of an isolated mass of a compressible fluid. Zbl 1118.76312
Denisova, I. V.; Solonnikov, V. A.
2000
Jeffery-Hamel asymptotics for steady state Navier-Stokes flow in domains with sector-like outlets to infinity. Zbl 0979.35113
Rivkind, L.; Solonnikov, V. A.
2000
On the quasistationary approximation in the problem of evolution of an isolated liquid mass. Zbl 0961.35115
Solonnikov, V. A.
2000
$$L_p$$-estimates for solutions to the initial-boundary value problem for the generalized Stokes system of equations in a bounded domain. Zbl 0986.35084
Solonnikov, V. A.
2000
The initial-boundary value problem for a generalized Stokes system in a half-space. Zbl 1027.76010
Solonnikov, V. A.
2000
On nonsymmetric two-dimensional viscous flow through an aperture. Zbl 0977.76014
Rivkind, L. P.; Solonnikov, V. A.
2000
A one-dimensional parabolic problem arising in studies of some free boundary problems. Zbl 1031.35153
Solonnikov, V. A.; Fasano, A.
2000
On a parabolic system with time derivative in the boundary conditions and related free boundary problems. Zbl 0940.35211
Rodrigues, J. F.; Solonnikov, V. A.; Yi, F.
1999
On the justification of the quasistationary approximation in the problem of motion of a viscous capillary drop. Zbl 0974.35097
Solonnikov, V. A.
1999
Estimates for the solution of the second initial boundary-value problem for the Stokes system in the spaces of functions having Hölder continuous derivatives with respect to the spatial variables. Zbl 1153.76349
Solonnikov, V. A.
1999
On quasistationary approximation in the problem of motion of a capillary drop. Zbl 0919.35103
Solonnikov, V. A.
1999
On the problem of a steady fall of a drop in a liquid medium. Zbl 0951.35110
Solonnikov, V. A.
1999
Existence and regularity results for oblique derivative problems for heat equations in an angle. Zbl 0958.35063
Garroni, M. G.; Solonnikov, V. A.; Vivaldi, M. A.
1998
Solvability of two-dimensional free boundary value problem for the Navier-Stokes equations for limiting values of contact angle. Zbl 0932.35161
Solonnikov, Vsevolod A.
1998
Stationary free boundary problems for the Navier-Stokes equations. Zbl 0941.35071
Solonnikov, Vsevolod A.
1998
Free boundary problems for second order parabolic equations. Zbl 0922.35192
Solonnikov, V. A.
1998
Free boundary problem in the flow of a fluid at the exit of a cylindrical tube. (Problème de frontière libre dans l’écoulement d’un fluide à la sortie d’un tube cylindrique.) Zbl 0934.35127
Solonnikov, V. A.
1998
Recent developments in partial differential equations. Zbl 0910.00019
Solonnikov, Vsevolod A.
1998
Solvability of two stationary free boundary problems for the Navier-Stokes equations. Zbl 0955.35059
Solonnikov, V. A.
1998
On nonstationary Stokes problem in exterior domains. Zbl 0958.35103
Maremonti, P.; Solonnikov, V. A.
1997
$$L_p$$-theory for the Stefan problem. Zbl 0906.35119
Solonnikov, V. A.; Frolova, E. V.
1997
Gradient estimates for solutions of the Navier-Stokes equations. Zbl 0896.35104
Finn, Robert; Solonnikov, Vsevolod
1997
An estimate of the solutions of a stationary problem for the Navier-Stokes equations. Zbl 0961.35114
Solonnikov, V. A.
1997
Problem of steady motion for a second-grade fluid in the Hölder classes of functions. Zbl 0906.35075
Moghilevskii, I. Sh.; Solonnikov, V. A.
1997
Investigation of the problem of the flow of a compressible viscous fluid past a bounded body in the Hölder classes of functions. Zbl 0982.76544
Novotny, A.; Penel, P.; Solonnikov, V. A.
1997
Green function for the heat equation with oblique boundary conditions in an angle. Zbl 1011.35069
Garroni, Maria Giovanna; Solonnikov, Vsevolod Alekseevič; Vivaldi, Maria Agostina
1997
Existence, uniqueness and asymptotic behaviour of solutions of steady-state Navier-Stokes equations in a plane aperture domain. Zbl 0990.35116
Galdi, G. P.; Padula, M.; Solonnikov, V. A.
1996
On the oblique derivative problem in an infinite angle. Zbl 0897.35023
Garroni, M. G.; Solonnikov, V. A.; Vivaldi, M. A.
1996
Estimates of Oseen’s potentials in weighted Hölder spaces. Zbl 0857.76028
Solonnikov, V. A.
1996
On steady motion of a drop in an infinite liquid medium. Zbl 0928.76027
Solonnikov, V. A.
1996
Estimates for solutions of the nonstationary Stokes problem in anisotropic Sobolev spaces with mixed norm. Zbl 0909.35105
Maremonti, P.; Solonnikov, V. A.
1995
On some free boundary problems for the Navier-Stokes equations with moving contact points and lines. Zbl 0926.35116
Solonnikov, V. A.
1995
Classical solvability of the problem on the motion of two viscous incompressible fluids. Zbl 0859.35093
Denisova, I. V.; Solonnikov, V. A.
1995
...and 148 more Documents
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#### Cited by 2,029 Authors

 76 Solonnikov, Vsevolod Alekseevich 39 Pileckas, Konstantin 33 Maremonti, Paolo 28 Zajączkowski, Wojciech M. 20 Seregin, Gregory A. 19 Beirão da Veiga, Hugo 19 Giga, Yoshikazu 19 Repin, Sergeĭ Igorevich 19 Shibata, Yoshihiro 18 Farwig, Reinhard 18 Sohr, Hermann 16 Jin, Bum Ja 16 Mucha, Piotr Bogusław 16 Padula, Mariarosaria 15 Hieber, Matthias 14 Chang, Tongkeun 14 Tani, Atusi 13 Denisova, Irina Vlad. 13 Rojas-Medar, Marko Antonio 13 Shimizu, Senjo 12 Frolova, E. V. 12 Kamynin, Vitaly L. 11 Friedman, Avner 11 Galdi, Giovanni Paolo 11 Raymond, Jean-Pierre 10 Amrouche, Chérif 10 Degtyarev, Sergeĭ Petrovich 10 Deuring, Paul 10 Kang, Kyungkeun 10 Nazarov, Sergeĭ Aleksandrovich 9 Cherepova, M. F. 9 Choe, Hi Jun 9 Dong, Hongjie 9 Kozono, Hideo 9 O’Riordan, Eugene 9 Radkevich, Evgeniĭ Vladimirovich 9 Xin, Zhouping 8 Abels, Helmut 8 Amosov, Andreĭ Avenirovich 8 Ivanov, Aleksandr Vasil’evich 8 Ladyzhenskaya, Ol’ga Aleksandrovna 8 Maz’ya, Vladimir Gilelevich 8 Pukhnachov, Vladislav Vasil’evich 8 Russo, Remigio 8 Saal, Jürgen 8 Sritharan, Sivaguru S. 8 Tice, Ian 8 Zhang, Ping 7 Abe, Ken 7 Bazaliĭ, Boris V. 7 Berselli, Luigi Carlo 7 Borchers, Wolfgang 7 Braz e Silva, Pablo 7 Garroni, Maria Giovanna 7 Gracia, José Luis 7 Huang, Xiangdi 7 Johnsen, Jon 7 Kostin, Andrey B. 7 Maekawa, Yasunori 7 Málek, Josef 7 Mulone, Giuseppe 7 Nečasová, Šárka 7 Prüß, Jan Wilhelm 7 Rossmann, Jürgen 7 Shishkin, Grigoriĭ Ivanovich 7 Stupyalis, Lyudvikas I. 7 Tan, Zhong 7 Valli, Alberto 7 Vasylyeva, Nataliya V. 7 Vivaldi, Maria Agostina 7 Wang, Yanjin 7 Zlotnik, Alexander A. 6 Antontsev, Stanislav Nikolaevich 6 Arkhipova, Arina A. Arkhipova 6 Bazaliy, Borys V. 6 Danchin, Raphaël 6 Fan, Jishan 6 Grubb, Gerd 6 Han, Pigong 6 Hishida, Toshiaki 6 Kim, Hyunseok 6 Krasnoshchok, Mykola Valeriĭovych 6 Krylov, Nicolaĭ Vladimirovich 6 Lasiecka, Irena 6 Li, Jing 6 Meirmanov, Anvarbek Mukatovich 6 Novotný, Antonín 6 Ogawa, Takayoshi 6 Pyatkov, Sergeĭ Grigor’evich 6 Sequeira, Adélia 6 Shkoller, Steve 6 Šverák, Vladimír 6 Varnhorn, Werner 6 Vishnevskii, Mikhail P. 6 Wang, Lihe 6 Winkler, Michael 6 Yu, Haibo 6 Yuan, Hongjun 6 Zhang, Zhifei 5 Abdulla, Ugur G. ...and 1,929 more Authors
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#### Cited in 281 Serials

 164 Journal of Differential Equations 158 Journal of Mathematical Sciences (New York) 104 Journal of Mathematical Analysis and Applications 85 Siberian Mathematical Journal 68 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 62 Archive for Rational Mechanics and Analysis 56 Journal of Mathematical Fluid Mechanics 46 Ukrainian Mathematical Journal 40 Journal of Soviet Mathematics 39 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 38 Mathematical Notes 34 Nonlinear Analysis. Theory, Methods & Applications 33 Journal of Functional Analysis 32 Mathematical Methods in the Applied Sciences 28 Computers & Mathematics with Applications 27 Journal of Applied Mathematics and Mechanics 26 Rendiconti del Seminario Matematico della Università di Padova 26 Acta Applicandae Mathematicae 25 Communications in Mathematical Physics 25 SIAM Journal on Mathematical Analysis 25 Nonlinear Analysis. Real World Applications 23 Mathematische Annalen 23 Journal de Mathématiques Pures et Appliquées. Neuvième Série 22 Lithuanian Mathematical Journal 22 Communications in Partial Differential Equations 22 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 21 Mathematische Zeitschrift 21 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 19 Annali di Matematica Pura ed Applicata. Serie Quarta 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 18 Differential Equations 18 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 17 Journal of Computational and Applied Mathematics 17 Zeitschrift für Analysis und ihre Anwendungen 16 Applied Mathematics and Computation 16 St. Petersburg Mathematical Journal 15 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 13 Discrete and Continuous Dynamical Systems 13 Abstract and Applied Analysis 12 Proceedings of the Japan Academy. Series A 12 Applications of Mathematics 12 Boundary Value Problems 11 Applicable Analysis 11 Journal of Mathematical Physics 11 Applied Mathematics and Optimization 11 Journal of Evolution Equations 10 Manuscripta Mathematica 10 Mathematische Nachrichten 10 Transactions of the American Mathematical Society 10 Applied Mathematics Letters 10 Computational Mathematics and Mathematical Physics 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 9 Rocky Mountain Journal of Mathematics 9 Doklady Mathematics 9 Evolution Equations and Control Theory 8 Communications on Pure and Applied Mathematics 8 Numerische Mathematik 8 Stochastic Processes and their Applications 8 Communications on Pure and Applied Analysis 8 Discrete and Continuous Dynamical Systems. Series S 7 The Annals of Probability 7 RAIRO. Modélisation Mathématique et Analyse Numérique 7 Calculus of Variations and Partial Differential Equations 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 7 Science China. Mathematics 7 Journal of Siberian Federal University. Mathematics & Physics 6 Advances in Mathematics 6 Journal of the Mathematical Society of Japan 6 Journal of Optimization Theory and Applications 6 Sbornik: Mathematics 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 5 International Journal of Engineering Science 5 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 5 Meccanica 5 Proceedings of the American Mathematical Society 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Physica D 5 Applied Numerical Mathematics 5 Acta Mathematicae Applicatae Sinica. English Series 5 Journal of Integral Equations and Applications 5 Journal of Dynamics and Differential Equations 5 Russian Mathematics 5 Topological Methods in Nonlinear Analysis 5 NoDEA. Nonlinear Differential Equations and Applications 5 Journal of Applied Mechanics and Technical Physics 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Proceedings of the Steklov Institute of Mathematics 5 Analysis and Mathematical Physics 4 Journal d’Analyse Mathématique 4 Journal of Computational Physics 4 Nonlinearity 4 Mathematics of Computation 4 Acta Mathematica 4 Annales de l’Institut Fourier 4 Tohoku Mathematical Journal. Second Series 4 Mathematical and Computer Modelling 4 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 4 Japan Journal of Industrial and Applied Mathematics 4 The Annals of Applied Probability ...and 181 more Serials
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#### Cited in 42 Fields

 1,936 Partial differential equations (35-XX) 1,052 Fluid mechanics (76-XX) 146 Numerical analysis (65-XX) 103 Calculus of variations and optimal control; optimization (49-XX) 83 Operator theory (47-XX) 83 Biology and other natural sciences (92-XX) 81 Functional analysis (46-XX) 80 Mechanics of deformable solids (74-XX) 80 Classical thermodynamics, heat transfer (80-XX) 78 Probability theory and stochastic processes (60-XX) 69 Systems theory; control (93-XX) 34 Ordinary differential equations (34-XX) 27 Integral equations (45-XX) 24 Global analysis, analysis on manifolds (58-XX) 23 Dynamical systems and ergodic theory (37-XX) 22 Statistical mechanics, structure of matter (82-XX) 21 Geophysics (86-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 17 Potential theory (31-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Differential geometry (53-XX) 14 Optics, electromagnetic theory (78-XX) 11 Real functions (26-XX) 9 Functions of a complex variable (30-XX) 9 Astronomy and astrophysics (85-XX) 6 Computer science (68-XX) 5 History and biography (01-XX) 5 Mechanics of particles and systems (70-XX) 5 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Approximations and expansions (41-XX) 3 Statistics (62-XX) 3 Quantum theory (81-XX) 2 Difference and functional equations (39-XX) 2 Integral transforms, operational calculus (44-XX) 2 Relativity and gravitational theory (83-XX) 2 Information and communication theory, circuits (94-XX) 1 Algebraic geometry (14-XX) 1 Special functions (33-XX) 1 General topology (54-XX)

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