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The solvability of the second initial boundary-value problem for the linear, time-dependent system of Navier-Stokes equations. (English) Zbl 0388.35059

MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35B45 A priori estimates in context of PDEs
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[1] V. A. Solonnikov, ?Estimates of solutions of the time-dependent, linearized system of Navier-Stokes equations,? Tr. Mat. Inst. Akad. Nauk SSSR,70, 213?317 (1964).
[2] V. A. Solonnikov, ?Estimates of the solution of an initial boundary-value problem for the linear, time-dependent system of Navier-Stokes equations,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,59, 178?254 (1976).
[3] V. A. Solonnikov, ?On the differentiability properties of the solution of the first boundary-value problem for the time-dependent system of Navier-Stokes equations,? Tr. Mat. Inst. Akad. Nauk SSSR,73, 221?291 (1964).
[4] V. A. Solonnikov, ?Estimates of solutions of the time-dependent Navier-Stokes system,? Zap. Nauchn. Sem. Lenigr. Otd. Mat. Inst. Akad. Nauk SSSR,38, 153?231 (1973).
[5] S. Agmon, A. Douglis, and L. Nirenberg, ?Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II,? Comm. Pure Appl. Math.,17, 35?92 (1964). · Zbl 0123.28706 · doi:10.1002/cpa.3160170104
[6] L. P. Volevich, ?The solvability.of boundary-value problems for general elliptic systems,? Mat. Sb.,68, 373?416 (1965).
[7] V. A. Solonnikov, ?On general boundary-value problems for systems which are elliptic in the sense of A. Douglis and L. Nirenberg,? Tr. Mat. Inst. Akad. Nauk SSSR,92, 233?298 (1966).
[8] O. A. Ladyzhenskaya, Mathematical Theory of Viscous Incompressible Flow, Gordon (1969). · Zbl 0184.52603
[9] V. A. Solonnikov and V. E. Shchadilov, ?On a boundary-value problem for the stationary system of Navier-Stokes equations,? Tr. Mat. Inst. Akad. Nauk SSSR,125, 196?210 (1973).
[10] V. A. Solonnikov, ?On boundary-value problems for linear parabolic systems of differential equations of general type,? Tr. Mat. Inst. Akad. Nauk SSSR,83, 3?162 (1965). · Zbl 0164.12502
[11] O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Plenum Publ. (1971). · Zbl 0169.00206
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