Edit Profile (opens in new tab) Farwig, Reinhard Co-Author Distance Author ID: farwig.reinhard Published as: Farwig, Reinhard; Farwig, R. Homepage: http://www3.mathematik.tu-darmstadt.de/hp/ag-analysis/farwig-reinhard/prof-dr-re... External Links: MGP · ResearchGate · dblp · GND Documents Indexed: 127 Publications since 1981, including 1 Additional arXiv Preprint 3 Contributions as Editor Co-Authors: 41 Co-Authors with 103 Joint Publications 748 Co-Co-Authors all top 5 Co-Authors 26 single-authored 35 Sohr, Hermann 19 Kozono, Hideo 8 Neustupa, Jiří 7 Nečasová, Šárka 6 Taniuchi, Yasushi 6 Varnhorn, Werner 5 Hishida, Toshiaki 5 Ri, Myong-Hwan 4 Galdi, Giovanni Paolo 4 Giga, Yoshikazu 4 Qian, Chenyin 4 Tsuda, Kazuyuki 4 Wegmann, David 3 Hsu, Pen-Yuan 3 Krbec, Miroslav 3 Penel, Patrick 3 Riechwald, Paul Felix 3 Rosteck, Veronika 3 Zwick, Daniel S. 2 Danchin, Raphaël 2 Komo, Christian 2 Myong-Hwan, Ri 2 Nakatsuka, Tomoyuki 2 Pokorný, Milan 2 Schulz, Raphael 2 Simader, Christian Georg 1 Guenther, Ronald B. 1 Iwabuchi, Tsukasa 1 Kanamaru, Ryo 1 Kračmar, Stanislav 1 Kyed, Mads 1 Marschall, Erich 1 Morimoto, Hiroko 1 Müller, Detlef 1 Novotný, Antonín 1 Okabe, Takahiro 1 Sauer, Jonas 1 Thomann, Enrique A. 1 Yamazaki, Masao 1 Yanagisawa, Taku 1 Zhang, Ping all top 5 Serials 6 Journal of Mathematical Fluid Mechanics 5 Archiv der Mathematik 5 Journal of the Mathematical Society of Japan 5 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 4 Journal of Mathematical Analysis and Applications 4 Mathematical Methods in the Applied Sciences 4 Journal of Evolution Equations 3 Funkcialaj Ekvacioj. Serio Internacia 3 Hokkaido Mathematical Journal 3 Journal of Differential Equations 3 Manuscripta Mathematica 3 Mathematische Annalen 3 Mathematische Nachrichten 3 NoDEA. Nonlinear Differential Equations and Applications 3 Discrete and Continuous Dynamical Systems. Series S 3 Journal of Elliptic and Parabolic Equations 2 Applicable Analysis 2 Indiana University Mathematics Journal 2 Integral Equations and Operator Theory 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 2 Tôhoku Mathematical Journal. Second Series 2 Zeitschrift für Analysis und ihre Anwendungen 2 Communications in Partial Differential Equations 2 Advances in Differential Equations 2 Analysis (München) 2 RIMS Kôkyûroku Bessatsu 1 American Mathematical Monthly 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Mathematische Semesterberichte 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Studia Mathematica 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Acta Mathematica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Czechoslovak Mathematical Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Functional Analysis 1 Journal of the Korean Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matematico della Università di Padova 1 SIAM Journal on Numerical Analysis 1 Tokyo Journal of Mathematics 1 Analysis 1 Acta Applicandae Mathematicae 1 Asymptotic Analysis 1 Mathematica Bohemica 1 Topological Methods in Nonlinear Analysis 1 Bulletin des Sciences Mathématiques 1 Discrete and Continuous Dynamical Systems 1 Nonlinear Analysis. Real World Applications 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Contemporary Mathematics 1 Advances in Nonlinear Analysis 1 SN Partial Differential Equations and Applications all top 5 Fields 116 Partial differential equations (35-XX) 100 Fluid mechanics (76-XX) 14 Operator theory (47-XX) 10 Functional analysis (46-XX) 7 Approximations and expansions (41-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 4 General and overarching topics; collections (00-XX) 4 Numerical analysis (65-XX) 3 Real functions (26-XX) 2 History and biography (01-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Mechanics of deformable solids (74-XX) 2 Geophysics (86-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 114 Publications have been cited 1,499 times in 702 Documents Cited by ▼ Year ▼ Generalized resolvent estimates for the Stokes system in bounded and unbounded domains. Zbl 0819.35109 Farwig, Reinhard; Sohr, Hermann 92 1994 An \(L^q\)-approach to Stokes and Navier-Stokes equations in general domains. Zbl 1111.35033 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 79 2005 Weighted \(L^q\)-theory for the Stokes resolvent in exterior domains. Zbl 0918.35106 Farwig, Reinhard; Sohr, Hermann 59 1997 The stationary exterior 3D-problem of Oseen and Navier-Stokes equations in anisotropically weighted spaces. Zbl 0727.35106 Farwig, Reinhard 55 1992 A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data. Zbl 1104.35032 Farwig, Reinhard; Galdi, Giovanni P.; Sohr, Hermann 49 2006 An \(L^q\)-analysis of viscous fluid flow past a rotating obstacle. Zbl 1136.76340 Farwig, Reinhard 47 2006 \(L^q\)-theory of a singular ”winding” integral operator arising from fluid dynamics. Zbl 1057.35028 Farwig, Reinhard; Hishida, Toshiaki; Müller, Detlef 45 2004 Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data. Zbl 1107.76022 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 37 2007 Rate of convergence of Shepard’s global interpolation formula. Zbl 0607.41005 Farwig, Reinhard 35 1986 On the Helmholtz decomposition in general unbounded domains. Zbl 1121.35097 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 35 2007 Stationary Navier-Stokes flow around a rotating obstacle. Zbl 1180.35408 Farwig, Reinhard; Hishida, Toshiaki 33 2007 On optimal initial value conditions for local strong solutions of the Navier-Stokes equations. Zbl 1179.35210 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 32 2009 Helmholtz decomposition and Stokes resolvent system for aperture domains in \(L^ q\)-spaces. Zbl 0847.35101 Farwig, Reinhard; Sohr, Hermann 29 1996 On the spectrum of a Stokes-type operator arising from flow around a rotating body. Zbl 1126.35050 Farwig, Reinhard; Neustupa, Jiří 29 2007 Very weak solutions and large uniqueness classes of stationary Navier-Stokes equations in bounded domains of \(\mathbb R^2\). Zbl 1119.35045 Farwig, R.; Galdi, G. P.; Sohr, H. 28 2006 Stationary solutions of compressible Navier-Stokes equations with slip boundary condition. Zbl 0701.35127 Farwig, Reinhard 27 1989 Weighted estimates for the Oseen equations and the Navier-Stokes equations in exterior domains. Zbl 0934.35120 Farwig, Reinhard; Sohr, Hermann 27 1998 On the Stokes operator in general unbounded domains. Zbl 1170.76011 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 24 2009 Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle. Zbl 1101.35348 Farwig, Reinhard 23 2005 Optimal initial value conditions for the existence of local strong solutions of the Navier-Stokes equations. Zbl 1173.35096 Farwig, Reinhard; Sohr, Hermann 23 2009 Asymptotic structure of a Leray solution to the Navier-Stokes flow around a rotating body. Zbl 1234.35035 Farwig, Reinhard; Galdi, Giovanni P.; Kyed, Mads 22 2011 Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle. Zbl 1229.35173 Farwig, Reinhard; Hishida, Toshiaki 21 2011 Very weak solutions of stationary and instationary Navier-Stokes equations with nonhomogeneous data. Zbl 1246.35148 Farwig, Reinhard; Galdi, Giovanni P.; Sohr, Hermann 21 2005 A weighted \(L^q\)-approach to Oseen flow around a rotating body. Zbl 1132.76015 Farwig, R.; Krbec, M.; Nečasová, Š. 19 2008 The stationary Navier-Stokes equations in a 3D-exterior domain. Zbl 0941.35064 Farwig, Reinhard 18 1998 Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions. Zbl 1205.35192 Farwig, Reinhard; Okabe, Takahiro 18 2010 A note on the reflection principle for the biharmonic equation and the Stokes system. Zbl 0815.31002 Farwig, Reinhard 18 1994 Asymptotic profile of steady Stokes flow around a rotating obstacle. Zbl 1229.35172 Farwig, Reinhard; Hishida, Toshiaki 18 2011 Global estimates in weighted spaces of weak solutions of the Navier-Stokes equations in exterior domains. Zbl 0855.35099 Farwig, R.; Sohr, H. 17 1996 On the energy equality of Navier-Stokes equations in general unbounded domains. Zbl 1202.35169 Farwig, Reinhard; Taniuchi, Yasushi 17 2010 Multivariate interpolation of arbitrarily spaced data by moving least squares methods. Zbl 0636.65007 Farwig, Reinhard 17 1986 Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in \(\mathbb R^n\). Zbl 1224.76034 Farwig, R.; Sohr, H. 15 2009 A weighted \(L^q\)-approach to Stokes flow around a rotating body. Zbl 1248.35158 Farwig, Reinhard; Krbec, Miroslav; Nečasová, Šárka 15 2008 Spectral properties in \(L^q\) of an Oseen operator modelling fluid flow past a rotating body. Zbl 1194.35324 Farwig, Reinhard; Neustupa, Jiří 15 2010 Initial values for the Navier-Stokes equations in spaces with weights in time. Zbl 1364.35236 Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan 14 2016 Resolvent estimates and maximal regularity in weighted \(L^{q}\)-spaces of the Stokes operator in an infinite cylinder. Zbl 1162.76322 Farwig, Reinhard; Myong-Hwan, Ri 13 2008 Local in time regularity properties of the Navier-Stokes equations. Zbl 1175.35100 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 13 2007 Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle. Zbl 1205.35191 Farwig, Reinhard; Hishida, Toshiaki 13 2009 On the Stokes and Navier-Stokes system for domains with noncompact boundary in \(L^ q\)-spaces. Zbl 0836.35117 Farwig, Reinhard; Sohr, Hermann 12 1994 On the spectrum of an Oseen-type operator arising from flow past a rotating body. Zbl 1180.35382 Farwig, Reinhard; Neustupa, Jiří 12 2008 Some divided difference inequalities for n-convex functions. Zbl 0579.41011 Farwig, R.; Zwick, D. 11 1985 Extensions of Serrin’s uniqueness and regularity conditions for the Navier-Stokes equations. Zbl 1254.76053 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 11 2012 Weighted \(L^q\)-Helmholtz decompositions in infinite cylinders and in infinite layers. Zbl 1038.35068 Farwig, Reinhard 10 2003 Weighted energy inequalities for the Navier-Stokes equations in exterior domains. Zbl 0833.35107 Farwig, Reinhard; Sohr, Hermann 10 1995 Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence. Zbl 1236.35103 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 10 2011 The Navier-Stokes equations with initial values in Besov spaces of type \(B^{-1+3/q}_{q,\infty}\). Zbl 1390.35229 Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan 10 2017 Weak solutions of the Navier-Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality. Zbl 1285.35065 Farwig, Reinhard; Kozono, Hideo 9 2014 Regularity of weak solutions to the Navier-Stokes equations in exterior domains. Zbl 1189.76115 Farwig, Reinhard; Komo, Christian 9 2010 The resolvent problem and \(H^\infty\)-calculus of the Stokes operator in unbounded cylinders with several exits to infinity. Zbl 1170.35073 Farwig, Reinhard; Myong-Hwan, Ri 9 2007 Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in \(L^3\). Zbl 1321.35133 Farwig, Reinhard; Nakatsuka, Tomoyuki; Taniuchi, Yasushi 8 2015 Maximal regularity of the Stokes operator in general unbounded domains of \(\mathbb R^n\). Zbl 1171.35448 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 8 2008 Spectral analysis of a Stokes-type operator arising from flow around a rotating body. Zbl 1223.35257 Farwig, Reinhard; Nečasová, Šárka; Neustupa, Jiří 8 2011 Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in \(\mathbb{R}^2\). Zbl 1409.35034 Farwig, Reinhard; Qian, Chenyin 8 2019 Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. Zbl 1231.35145 Farwig, Reinhard; Taniuchi, Yasushi 8 2011 A variational approach in weighted Sobolev spaces to the operator \(- \Delta +\partial /\partial x_ 1\) in exterior domains of \({\mathbb{R}}^ 3\). Zbl 0727.35041 Farwig, Reinhard 8 1992 Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains. Zbl 1341.35098 Farwig, Reinhard; Rosteck, Veronika 7 2016 On regularity of weak solutions to the instationary Navier-Stokes system: a review on recent results. Zbl 1304.35484 Farwig, Reinhard 7 2014 Uniqueness of solutions on the whole time axis to the Navier-Stokes equations in unbounded domains. Zbl 1334.35203 Farwig, Reinhard; Nakatsuka, Tomoyuki; Taniuchi, Yasushi 7 2015 Stokes resolvent systems in an infinite cylinder. Zbl 1131.35055 Farwig, Reinhard; Ri, Myong-Hwan 7 2007 The stationary and non-stationary Stokes system in exterior domains with non-zero divergence and non-zero boundary values. Zbl 0798.35125 Farwig, Reinhard; Sohr, Hermann 7 1994 Very weak solutions to the Navier-Stokes system in general unbounded domains. Zbl 1328.35010 Farwig, Reinhard; Riechwald, Paul Felix 6 2015 Multivariate interpolation of scattered data by moving least squares methods. Zbl 0615.41001 Farwig, R. 6 1987 Partial regularity and weighted energy estimates of global weak solutions of the Navier-Stokes system. Zbl 0865.35100 Farwig, R. 6 1996 Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin’s condition. Zbl 1154.35416 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 6 2008 Uniqueness of backward asymptotically almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. Zbl 1260.35109 Farwig, Reinhard; Taniuchi, Yasushi 6 2013 On the existence of local strong solutions for the Navier-Stokes equations in completely general domains. Zbl 1194.35306 Farwig, Reinhard; Sohr, Hermann 6 2010 On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces. Zbl 1428.35285 Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan 6 2019 The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body. Zbl 1280.35087 Farwig, Reinhard; Guenther, Ronald B.; Thomann, Enrique A.; Nečasová, Šarka 6 2014 Global Leray-Hopf weak solutions of the Navier-Stokes equations with nonzero time-dependent boundary values. Zbl 1247.35090 Farwig, R.; Kozono, H.; Sohr, H. 6 2011 An approach to resolvent estimates for the Stokes equations in \(L^ q\)- spaces. Zbl 0779.35087 Farwig, Reinhard; Sohr, Hermann 5 1992 Energy-based regularity criteria for the Navier-Stokes equations. Zbl 1185.35162 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 5 2009 Existence and exponential stability in \(L^{r}\)-spaces of stationary Navier-Stokes flows with prescribed flux in infinite cylindrical domains. Zbl 1127.35040 Ri, Myong-Hwan; Farwig, Reinhard 5 2007 On the essential spectrum of a Stokes-type operator arising from flow around a rotating body in the \(L^q\)-framework. Zbl 1119.35046 Farwig, Reinhard; Neǎsová, Šárka; Neustupa, Jiří 5 2007 Necessary and sufficient conditions on local strong solvability of the Navier-Stokes system. Zbl 1209.35096 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 5 2011 Global weak solutions of the Navier-Stokes system with nonzero boundary conditions. Zbl 1291.35030 Farwig, R.; Kozono, H.; Sohr, H. 5 2010 Note on the flux condition and pressure drop in the resolvent problem of the Stokes system. Zbl 0847.35102 Farwig, Reinhard 5 1996 Incompressible inhomogeneous fluids in bounded domains of \(\mathbb{R}^3\) with bounded density. Zbl 1433.35222 Farwig, Reinhard; Qian, Chenyin; Zhang, Ping 5 2020 The time periodic problem of the Navier-Stokes equations in a bounded domain with moving boundary. Zbl 1478.35167 Farwig, Reinhard; Kozono, Hideo; Tsuda, Kazuyuki; Wegmann, David 5 2021 Optimal initial value conditions for local strong solutions of the Navier-Stokes equations in exterior domains. Zbl 1274.76189 Farwig, Reinhard; Komo, Christian 5 2013 Leray’s inequality in general multi-connected domains in \({\mathbb{R}^n}\). Zbl 1248.35142 Farwig, Reinhard; Kozono, Hideo; Yanagisawa, Taku 5 2012 Besov space regularity conditions for weak solutions of the Navier-Stokes equations. Zbl 1291.35177 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 4 2014 The Stokes resolvent problem in general unbounded domains. Zbl 1127.35035 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 4 2007 Note on Friedrichs’ inequality in \(N\)-star-shaped domains. Zbl 1342.26054 Farwig, Reinhard; Rosteck, Veronika 4 2016 Regularity criteria for weak solutions of the Navier-Stokes system in general unbounded domains. Zbl 1342.35226 Riechwald, Paul Felix; Farwig, Reinhard 4 2016 Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier-Stokes equations. Zbl 1428.35286 Farwig, Reinhard; Kozono, Hideo; Wegmann, David 4 2019 Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness. Zbl 1397.35170 Farwig, Reinhard; Giga, Yoshikazu 4 2018 Optimality of Serrin type extension criteria to the Navier-Stokes equations. Zbl 1473.35400 Farwig, Reinhard; Kanamaru, Ryo 4 2021 An \(L^ q\)-theory for weak solutions of the Stokes system in exterior domains. Zbl 0787.35063 Farwig, R.; Simader, C. G.; Sohr, H. 3 1993 Multivariate truncated powers and B-splines with coalescent knots. Zbl 0573.41023 Farwig, R. 3 1985 Regularity of weak solutions for the Navier-Stokes equations via energy criteria. Zbl 1374.35280 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 3 2010 From Jean Leray to the millennium problem: the Navier-Stokes equations. Zbl 1492.35002 Farwig, Reinhard 3 2021 Existence of strong solutions and decay of turbulent solutions of Navier-Stokes flow with nonzero Dirichlet boundary data. Zbl 1367.35107 Farwig, Reinhard; Kozono, Hideo; Wegmann, David 3 2017 Leray’s inequality for fluid flow in symmetric multi-connected two-dimensional domains. Zbl 1256.35053 Farwig, Reinhard; Morimoto, Hiroko 3 2012 Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains. Zbl 1333.35162 Farwig, Reinhard; Riechwald, Paul Felix 2 2015 Very weak solutions of the stationary Stokes equations in unbounded domains of half space type. Zbl 1349.76055 Farwig, Reinhard; Sauer, Jonas 2 2015 The weak Neumann problem and the Helmholtz decomposition in general aperture domains. Zbl 0806.35021 Farwig, R. 2 1993 An \(L^q(L^2)\)-theory of the generalized Stokes resolvent system in infinite cylinders. Zbl 1111.35034 Farwig, Reinhard; Ri, Myong-Hwan 2 2007 The fundamental solution of a modified Oseen problem. Zbl 0969.35005 Farwig, R.; Novotný, A.; Pokorný, M. 2 2000 On the type of spectral operators and the non-spectrality of several differential operators on \(L^ p\). Zbl 0473.47018 Farwig, Reinhard; Marschall, Erich 2 1981 Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders. Zbl 1321.35140 Ri, Myong-Hwan; Farwig, Reinhard 2 2015 Maximal \(L^1\)-regularity of generators for bounded analytic semigroups in Banach spaces. Zbl 1499.46050 Ri, Myong-Hwan; Farwig, Reinhard 2 2022 The Fujita-Kato approach for the Navier-Stokes equations with moving boundary and its application. Zbl 1493.35065 Farwig, Reinhard; Tsuda, Kazuyuki 2 2022 The time periodic problem of the Navier-Stokes equations in a bounded domain with moving boundary. Zbl 1478.35167 Farwig, Reinhard; Kozono, Hideo; Tsuda, Kazuyuki; Wegmann, David 5 2021 Optimality of Serrin type extension criteria to the Navier-Stokes equations. Zbl 1473.35400 Farwig, Reinhard; Kanamaru, Ryo 4 2021 From Jean Leray to the millennium problem: the Navier-Stokes equations. Zbl 1492.35002 Farwig, Reinhard 3 2021 Uniform estimates for fractional operators. Zbl 1464.35176 Farwig, Reinhard; Tsuda, Kazuyuki 2 2021 Incompressible inhomogeneous fluids in bounded domains of \(\mathbb{R}^3\) with bounded density. Zbl 1433.35222 Farwig, Reinhard; Qian, Chenyin; Zhang, Ping 5 2020 Asymptotic behavior for the quasi-geostrophic equations with fractional dissipation in \(\mathbb{R}^2\). Zbl 1409.35034 Farwig, Reinhard; Qian, Chenyin 8 2019 On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces. Zbl 1428.35285 Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan 6 2019 Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier-Stokes equations. Zbl 1428.35286 Farwig, Reinhard; Kozono, Hideo; Wegmann, David 4 2019 Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains. Zbl 1434.35049 Farwig, Reinhard; Rosteck, Veronika 1 2019 Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness. Zbl 1397.35170 Farwig, Reinhard; Giga, Yoshikazu 4 2018 Mathematical analysis in fluid mechanics: selected recent results. International conference on vorticity, rotation and symmetry (IV) – complex fluids and the issue of regularity, CIRM, Luminy, Marseille, France, May 8–12, 2017. Proceedings. Zbl 1396.35001 2 2018 Spatial asymptotic profiles of solutions to the Navier-Stokes system in a rotating frame with fast decaying data. Zbl 1401.76159 Farwig, Reinhard; Schulz, Raphael; Taniuchi, Yasushi 1 2018 The Navier-Stokes equations with initial values in Besov spaces of type \(B^{-1+3/q}_{q,\infty}\). Zbl 1390.35229 Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan 10 2017 Existence of strong solutions and decay of turbulent solutions of Navier-Stokes flow with nonzero Dirichlet boundary data. Zbl 1367.35107 Farwig, Reinhard; Kozono, Hideo; Wegmann, David 3 2017 Decay of non-stationary Navier-Stokes flow with nonzero Dirichlet boundary data. Zbl 1390.35238 Wegmann, David; Farwig, Reinhard; Kozono, Hideo 2 2017 Jean Leray: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63 (1934), 193–248. Zbl 1373.76004 Farwig, Reinhard 1 2017 Initial values for the Navier-Stokes equations in spaces with weights in time. Zbl 1364.35236 Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan 14 2016 Resolvent estimates of the Stokes system with Navier boundary conditions in general unbounded domains. Zbl 1341.35098 Farwig, Reinhard; Rosteck, Veronika 7 2016 Note on Friedrichs’ inequality in \(N\)-star-shaped domains. Zbl 1342.26054 Farwig, Reinhard; Rosteck, Veronika 4 2016 Regularity criteria for weak solutions of the Navier-Stokes system in general unbounded domains. Zbl 1342.35226 Riechwald, Paul Felix; Farwig, Reinhard 4 2016 General properties of the Helmholtz decomposition in spaces of \(L^q\)-type. Zbl 1349.35292 Farwig, Reinhard; Simader, Christian; Sohr, Hermann; Varnhorn, Werner 2 2016 Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in \(L^3\). Zbl 1321.35133 Farwig, Reinhard; Nakatsuka, Tomoyuki; Taniuchi, Yasushi 8 2015 Uniqueness of solutions on the whole time axis to the Navier-Stokes equations in unbounded domains. Zbl 1334.35203 Farwig, Reinhard; Nakatsuka, Tomoyuki; Taniuchi, Yasushi 7 2015 Very weak solutions to the Navier-Stokes system in general unbounded domains. Zbl 1328.35010 Farwig, Reinhard; Riechwald, Paul Felix 6 2015 Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains. Zbl 1333.35162 Farwig, Reinhard; Riechwald, Paul Felix 2 2015 Very weak solutions of the stationary Stokes equations in unbounded domains of half space type. Zbl 1349.76055 Farwig, Reinhard; Sauer, Jonas 2 2015 Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders. Zbl 1321.35140 Ri, Myong-Hwan; Farwig, Reinhard 2 2015 A linearized model for compressible flow past a rotating obstacle: analysis via modified Bochner-Riesz multipliers. Zbl 1325.35163 Farwig, Reinhard; Pokorný, Milan 2 2015 Local strong solutions of the nonhomogeneous Navier-Stokes system with control of the interval of existence. Zbl 1362.35207 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 1 2015 Weak solutions of the Navier-Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality. Zbl 1285.35065 Farwig, Reinhard; Kozono, Hideo 9 2014 On regularity of weak solutions to the instationary Navier-Stokes system: a review on recent results. Zbl 1304.35484 Farwig, Reinhard 7 2014 The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body. Zbl 1280.35087 Farwig, Reinhard; Guenther, Ronald B.; Thomann, Enrique A.; Nečasová, Šarka 6 2014 Besov space regularity conditions for weak solutions of the Navier-Stokes equations. Zbl 1291.35177 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 4 2014 Concentration-diffusion phenomena of heat convection in an incompressible fluid. Zbl 1294.35095 Farwig, Reinhard; Schulz, Raphael; Yamazaki, Masao 1 2014 Uniqueness of backward asymptotically almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. Zbl 1260.35109 Farwig, Reinhard; Taniuchi, Yasushi 6 2013 Optimal initial value conditions for local strong solutions of the Navier-Stokes equations in exterior domains. Zbl 1274.76189 Farwig, Reinhard; Komo, Christian 5 2013 Extensions of Serrin’s uniqueness and regularity conditions for the Navier-Stokes equations. Zbl 1254.76053 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 11 2012 Leray’s inequality in general multi-connected domains in \({\mathbb{R}^n}\). Zbl 1248.35142 Farwig, Reinhard; Kozono, Hideo; Yanagisawa, Taku 5 2012 Leray’s inequality for fluid flow in symmetric multi-connected two-dimensional domains. Zbl 1256.35053 Farwig, Reinhard; Morimoto, Hiroko 3 2012 Asymptotic structure of a Leray solution to the Navier-Stokes flow around a rotating body. Zbl 1234.35035 Farwig, Reinhard; Galdi, Giovanni P.; Kyed, Mads 22 2011 Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle. Zbl 1229.35173 Farwig, Reinhard; Hishida, Toshiaki 21 2011 Asymptotic profile of steady Stokes flow around a rotating obstacle. Zbl 1229.35172 Farwig, Reinhard; Hishida, Toshiaki 18 2011 Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence. Zbl 1236.35103 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 10 2011 Spectral analysis of a Stokes-type operator arising from flow around a rotating body. Zbl 1223.35257 Farwig, Reinhard; Nečasová, Šárka; Neustupa, Jiří 8 2011 Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. Zbl 1231.35145 Farwig, Reinhard; Taniuchi, Yasushi 8 2011 Global Leray-Hopf weak solutions of the Navier-Stokes equations with nonzero time-dependent boundary values. Zbl 1247.35090 Farwig, R.; Kozono, H.; Sohr, H. 6 2011 Necessary and sufficient conditions on local strong solvability of the Navier-Stokes system. Zbl 1209.35096 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 5 2011 Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions. Zbl 1205.35192 Farwig, Reinhard; Okabe, Takahiro 18 2010 On the energy equality of Navier-Stokes equations in general unbounded domains. Zbl 1202.35169 Farwig, Reinhard; Taniuchi, Yasushi 17 2010 Spectral properties in \(L^q\) of an Oseen operator modelling fluid flow past a rotating body. Zbl 1194.35324 Farwig, Reinhard; Neustupa, Jiří 15 2010 Regularity of weak solutions to the Navier-Stokes equations in exterior domains. Zbl 1189.76115 Farwig, Reinhard; Komo, Christian 9 2010 On the existence of local strong solutions for the Navier-Stokes equations in completely general domains. Zbl 1194.35306 Farwig, Reinhard; Sohr, Hermann 6 2010 Global weak solutions of the Navier-Stokes system with nonzero boundary conditions. Zbl 1291.35030 Farwig, R.; Kozono, H.; Sohr, H. 5 2010 Regularity of weak solutions for the Navier-Stokes equations via energy criteria. Zbl 1374.35280 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 3 2010 On optimal initial value conditions for local strong solutions of the Navier-Stokes equations. Zbl 1179.35210 Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner 32 2009 On the Stokes operator in general unbounded domains. Zbl 1170.76011 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 24 2009 Optimal initial value conditions for the existence of local strong solutions of the Navier-Stokes equations. Zbl 1173.35096 Farwig, Reinhard; Sohr, Hermann 23 2009 Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in \(\mathbb R^n\). Zbl 1224.76034 Farwig, R.; Sohr, H. 15 2009 Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle. Zbl 1205.35191 Farwig, Reinhard; Hishida, Toshiaki 13 2009 Energy-based regularity criteria for the Navier-Stokes equations. Zbl 1185.35162 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 5 2009 Weighted \(L^2\) and \(L^q\) approaches to fluid flow past a rotating body. Zbl 1167.76048 Farwig, R.; Kračmar, S.; Krbec, M.; Nečasová, Š.; Penel, P. 2 2009 A weighted \(L^q\)-approach to Oseen flow around a rotating body. Zbl 1132.76015 Farwig, R.; Krbec, M.; Nečasová, Š. 19 2008 A weighted \(L^q\)-approach to Stokes flow around a rotating body. Zbl 1248.35158 Farwig, Reinhard; Krbec, Miroslav; Nečasová, Šárka 15 2008 Resolvent estimates and maximal regularity in weighted \(L^{q}\)-spaces of the Stokes operator in an infinite cylinder. Zbl 1162.76322 Farwig, Reinhard; Myong-Hwan, Ri 13 2008 On the spectrum of an Oseen-type operator arising from flow past a rotating body. Zbl 1180.35382 Farwig, Reinhard; Neustupa, Jiří 12 2008 Maximal regularity of the Stokes operator in general unbounded domains of \(\mathbb R^n\). Zbl 1171.35448 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 8 2008 Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin’s condition. Zbl 1154.35416 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 6 2008 Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data. Zbl 1107.76022 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 37 2007 On the Helmholtz decomposition in general unbounded domains. Zbl 1121.35097 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 35 2007 Stationary Navier-Stokes flow around a rotating obstacle. Zbl 1180.35408 Farwig, Reinhard; Hishida, Toshiaki 33 2007 On the spectrum of a Stokes-type operator arising from flow around a rotating body. Zbl 1126.35050 Farwig, Reinhard; Neustupa, Jiří 29 2007 Local in time regularity properties of the Navier-Stokes equations. Zbl 1175.35100 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 13 2007 The resolvent problem and \(H^\infty\)-calculus of the Stokes operator in unbounded cylinders with several exits to infinity. Zbl 1170.35073 Farwig, Reinhard; Myong-Hwan, Ri 9 2007 Stokes resolvent systems in an infinite cylinder. Zbl 1131.35055 Farwig, Reinhard; Ri, Myong-Hwan 7 2007 Existence and exponential stability in \(L^{r}\)-spaces of stationary Navier-Stokes flows with prescribed flux in infinite cylindrical domains. Zbl 1127.35040 Ri, Myong-Hwan; Farwig, Reinhard 5 2007 On the essential spectrum of a Stokes-type operator arising from flow around a rotating body in the \(L^q\)-framework. Zbl 1119.35046 Farwig, Reinhard; Neǎsová, Šárka; Neustupa, Jiří 5 2007 The Stokes resolvent problem in general unbounded domains. Zbl 1127.35035 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 4 2007 An \(L^q(L^2)\)-theory of the generalized Stokes resolvent system in infinite cylinders. Zbl 1111.35034 Farwig, Reinhard; Ri, Myong-Hwan 2 2007 A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data. Zbl 1104.35032 Farwig, Reinhard; Galdi, Giovanni P.; Sohr, Hermann 49 2006 An \(L^q\)-analysis of viscous fluid flow past a rotating obstacle. Zbl 1136.76340 Farwig, Reinhard 47 2006 Very weak solutions and large uniqueness classes of stationary Navier-Stokes equations in bounded domains of \(\mathbb R^2\). Zbl 1119.35045 Farwig, R.; Galdi, G. P.; Sohr, H. 28 2006 An \(L^q\)-approach to Stokes and Navier-Stokes equations in general domains. Zbl 1111.35033 Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann 79 2005 Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle. Zbl 1101.35348 Farwig, Reinhard 23 2005 Very weak solutions of stationary and instationary Navier-Stokes equations with nonhomogeneous data. Zbl 1246.35148 Farwig, Reinhard; Galdi, Giovanni P.; Sohr, Hermann 21 2005 \(L^q\)-theory of a singular ”winding” integral operator arising from fluid dynamics. Zbl 1057.35028 Farwig, Reinhard; Hishida, Toshiaki; Müller, Detlef 45 2004 Weighted \(L^q\)-Helmholtz decompositions in infinite cylinders and in infinite layers. Zbl 1038.35068 Farwig, Reinhard 10 2003 The fundamental solution of a modified Oseen problem. Zbl 0969.35005 Farwig, R.; Novotný, A.; Pokorný, M. 2 2000 Weighted estimates for the Oseen equations and the Navier-Stokes equations in exterior domains. Zbl 0934.35120 Farwig, Reinhard; Sohr, Hermann 27 1998 The stationary Navier-Stokes equations in a 3D-exterior domain. Zbl 0941.35064 Farwig, Reinhard 18 1998 Weighted \(L^q\)-theory for the Stokes resolvent in exterior domains. Zbl 0918.35106 Farwig, Reinhard; Sohr, Hermann 59 1997 Helmholtz decomposition and Stokes resolvent system for aperture domains in \(L^ q\)-spaces. Zbl 0847.35101 Farwig, Reinhard; Sohr, Hermann 29 1996 Global estimates in weighted spaces of weak solutions of the Navier-Stokes equations in exterior domains. Zbl 0855.35099 Farwig, R.; Sohr, H. 17 1996 Partial regularity and weighted energy estimates of global weak solutions of the Navier-Stokes system. Zbl 0865.35100 Farwig, R. 6 1996 Note on the flux condition and pressure drop in the resolvent problem of the Stokes system. Zbl 0847.35102 Farwig, Reinhard 5 1996 Weighted energy inequalities for the Navier-Stokes equations in exterior domains. Zbl 0833.35107 Farwig, Reinhard; Sohr, Hermann 10 1995 Generalized resolvent estimates for the Stokes system in bounded and unbounded domains. Zbl 0819.35109 Farwig, Reinhard; Sohr, Hermann 92 1994 A note on the reflection principle for the biharmonic equation and the Stokes system. Zbl 0815.31002 Farwig, Reinhard 18 1994 On the Stokes and Navier-Stokes system for domains with noncompact boundary in \(L^ q\)-spaces. Zbl 0836.35117 Farwig, Reinhard; Sohr, Hermann 12 1994 ...and 14 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 617 Authors 55 Farwig, Reinhard 26 Nečasová, Šárka 21 Amrouche, Chérif 20 Kozono, Hideo 19 Galdi, Giovanni Paolo 18 Deuring, Paul 18 Hishida, Toshiaki 16 Jin, Bumja 16 Sohr, Hermann 15 Dell’Accio, Francesco 14 Di Tommaso, Filomena 13 Giga, Yoshikazu 13 Neustupa, Jiří 12 Kračmar, Stanislav 12 Shimizu, Senjo 11 Maremonti, Paolo 11 Otárola, Enrique 10 Kyed, Mads 10 Taniuchi, Yasushi 9 Chang, Tongkeun 9 Novotný, Antonín 9 Razafison, Ulrich 9 Salgado, Abner J. 8 Abe, Ken 8 Bae, Hyeong-Ohk 8 Hieber, Matthias 8 Kim, Hyunseok 8 Matevosyan, Hovik A. 8 Meslameni, Mohamed 8 Schumacher, Katrin 8 Shibata, Yoshihiro 8 Silvestre, Ana Leonor 8 Varnhorn, Werner 7 Haroske, Dorothee D. 7 Maekawa, Yasunori 7 Medková, Dagmar 7 Qian, Chenyin 7 Wittwer, Peter 6 Crispo, Francesca 6 Han, Pigong 6 Heck, Horst 6 Kim, Dugyu 6 Nguyen Thieu Huy 6 Penel, Patrick 6 Pokorný, Milan 6 Ri, Myong-Hwan 5 Allendes, Alejandro 5 Berselli, Luigi Carlo 5 Feireisl, Eduard 5 Geissert, Matthias 5 He, Cheng 5 Komo, Christian 5 Kunstmann, Peer Christian 5 Mohan, Manil Thankamani 5 Nakatsuka, Tomoyuki 5 Pileckas, Konstantin 5 Riechwald, Paul Felix 5 Vu Thi Ngoc Ha 4 Abels, Helmut 4 Barker, Tobias 4 Bolkart, Martin 4 Della Vecchia, Biancamaria 4 Higaki, Mitsuo 4 Jin, Chunhua 4 Krbec, Miroslav 4 Kubo, Takayuki 4 Miura, Hideyuki 4 Mucha, Piotr Bogusław 4 Nouisser, Otheman 4 Okabe, Takahiro 4 Pečarić, Josip 4 Sauer, Jonas 4 Scitovski, Rudolf 4 Siar, Najoua 4 Skalák, Zdeněk 4 Suzuki, Takuya 4 Takahashi, Takéo 4 Vukelić, Ana 4 Wang, Yejuan 3 Albritton, Dallas 3 An, Rong 3 Benabidallah, Rachid 3 Bouzit, Hamid 3 Cătinaş, Teodora 3 Choe, Hi Jun 3 Duman, Oktay 3 Ebobisse, François Bille 3 Gu, Zhongyang 3 Guo, Zhengguang 3 Hayat, Tasawar 3 Kakizawa, Ryôhei 3 Kashiwabara, Takahito 3 Khai, D. Q. 3 Kobayashi, Takayuki 3 Konieczny, Paweł 3 Kreml, Ondřej 3 Li, Kaitai 3 Liang, Tongtong 3 Nguyễn Minh Trí 3 Piasecki, Tomasz ...and 517 more Authors all top 5 Cited in 170 Serials 54 Journal of Differential Equations 48 Journal of Mathematical Fluid Mechanics 27 Journal of Mathematical Analysis and Applications 26 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 24 Archive for Rational Mechanics and Analysis 24 Mathematical Methods in the Applied Sciences 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 22 Journal of Evolution Equations 19 Mathematische Nachrichten 17 Mathematische Annalen 13 Journal of Functional Analysis 13 Journal of the Mathematical Society of Japan 11 Journal of Computational and Applied Mathematics 8 Archiv der Mathematik 8 SIAM Journal on Mathematical Analysis 8 NoDEA. Nonlinear Differential Equations and Applications 8 Discrete and Continuous Dynamical Systems 7 ZAMP. 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Mathematica 1 Applied Mathematics and Optimization 1 BIT ...and 70 more Serials all top 5 Cited in 40 Fields 585 Partial differential equations (35-XX) 503 Fluid mechanics (76-XX) 70 Numerical analysis (65-XX) 41 Functional analysis (46-XX) 37 Approximations and expansions (41-XX) 35 Operator theory (47-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 21 Mechanics of deformable solids (74-XX) 15 Real functions (26-XX) 15 Biology and other natural sciences (92-XX) 14 Potential theory (31-XX) 14 Probability theory and stochastic processes (60-XX) 11 Geophysics (86-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Systems theory; control (93-XX) 6 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Integral equations (45-XX) 5 Functions of a complex variable (30-XX) 5 Mechanics of particles and systems (70-XX) 4 Computer science (68-XX) 4 Quantum theory (81-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Special functions (33-XX) 3 Abstract harmonic analysis (43-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Integral transforms, operational calculus (44-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year