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Uspekhi Mat. Nauk, 2003, Volume 58, Issue 2(350), Pages 123–156 (Mi umn613)  

This article is cited in 56 scientific papers (total in 56 papers)

On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator

V. A. Solonnikov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: In this paper, which is mainly of a survey nature, a coercive estimate is proved in Sobolev spaces with a mixed norm to solve the non-stationary Stokes problem (with non-zero divergence) in bounded and exterior domains, and from the first estimate an estimate is proved for the resolvent of the Stokes operator. The latter proof uses the explicit representation of the solution of the problem in a half-space in terms of the Green's matrix; pointwise estimates are derived for the elements of this matrix.

DOI: https://doi.org/10.4213/rm613

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English version:
Russian Mathematical Surveys, 2003, 58:2, 331–365

Bibliographic databases:

UDC: 517.9
MSC: Primary 35Q30; Secondary 35B45, 76D05, 46E35, 47A10, 34B27
Received: 15.02.2003

Citation: V. A. Solonnikov, “On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator”, Uspekhi Mat. Nauk, 58:2(350) (2003), 123–156; Russian Math. Surveys, 58:2 (2003), 331–365

Citation in format AMSBIB
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\paper On estimates of solutions of the non-stationary Stokes problem in anisotropic Sobolev spaces and on estimates for the resolvent of the Stokes operator
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