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Russian Mathematical Surveys, 2003, Volume 58, Issue 2, Pages 331–365
DOI: https://doi.org/10.1070/RM2003v058n02ABEH000613 (Mi rm613) 		 
This article is cited in 76 scientific papers (total in 76 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
English version PDF (346 kB) Citations (76)
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DOI: https://doi.org/10.1070/RM2003v058n02ABEH000613
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.
Received: 15.02.2003
Russian version:
Uspekhi Matematicheskikh Nauk, 2003, Volume 58, Issue 2(350), Pages 123–156
DOI: https://doi.org/10.4213/rm613
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 35Q30; Secondary 35B45, 76D05, 46E35, 47A10, 34B27
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 76 articles:
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