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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).

MSC:

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

Citations:

Zbl 0376.76021
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References:

[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).
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