Unique solvability of an initial- and boundary-value problem for viscous incompressible nonhomogeneous fluids. (English) Zbl 0401.76037

Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 52, 52–109 (1975; Zbl 0376.76021).


76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations


Zbl 0376.76021
Full Text: DOI


[1] S. N. Antontsev and A. V. Kazhikhov, The Mathematical Problems of the Dynamics of Non-homogeneous Fluids [in Russian], Novosibirsk (1973).
[2] O. A. Ladyzhenskaya, Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York (1969).
[3] O. A. Ladyzhenskaya (Ladyzenskaya), V. A. Solonnikov, and N. N. Ural’tseva (Ural’ceva), Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence (1968).
[4] Sh. Sakhaev and V. A. Solonnikov, ”Estimates of the solutions of a boundary-value problem of magnetohydrodynamics,” Tr. Mat. Inst., Akad. Nauk SSSR (1975). · Zbl 1261.35123
[5] S. Agmon, A. Douglis, and L. Nirenberg, ”Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I,” Comm. Pure Appl. Math.,12, 623–727 (1959). · Zbl 0093.10401
[6] V. A. Solonnikov, ”On a priori estimates for certain boundary-value problems,” Dokl. Akad. Nauk SSSR,138, 781–784 (1961).
[7] V. A. Solonnikov, ”Estimates of the solutions of nonstationary Navier-Stokes systems,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., Akad. Nauk SSSR,38, 152–231 (1973).
[8] V. A. Solonnikov, ”Estimates of the solutions of the nonstationary linearized Navier-Stokes equations,” Tr. Mat. Inst. Akad. Nauk SSSR,70, 213–317 (1964).
[9] V. P. Il’in, ”On the ’embedding’ theorems,” Tr. Mat. Inst., Akad. Nauk SSSR,53, 359–386 (1959).
[10] P. E. Sobolevskii, ”Coercivity inequalities for abstract parabolic equations,” Dokl. Akad. Nauk SSSR,157, 52–55 (1964).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.