Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem

Matthias Geissert; Matthias Hess; Matthias Georg Hieber; Céline Schwarz; Kyriakos Stavrakidis

doi:10.1007/s00021-008-0275-0

Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem

Matthias Geissert^*, Matthias Hess, Matthias Georg Hieber, Céline Schwarz, Kyriakos Stavrakidis

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

Introducing a new localization method involving Bogovskis operator we give a short and new proof for maximal L ^p - L ^q -estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an {\mathcal{R}} -sectorial operator in L{p}{\sigma}(\Omega), 1 <p <\infty, of {\mathcal{R}} -angle 0, for bounded or exterior domains of Ω.

Original language	English
Pages (from-to)	47-60
Number of pages	14
Journal	Journal of Mathematical Fluid Mechanics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1007/s00021-008-0275-0
Publication status	Published - 2010 Mar
Externally published	Yes

Keywords

Exterior domains
Maximal L - L -estimates
Stokes equation

ASJC Scopus subject areas

Applied Mathematics
Mathematical Physics
Computational Mathematics
Condensed Matter Physics

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10.1007/s00021-008-0275-0

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abstract = "Introducing a new localization method involving Bogovskis operator we give a short and new proof for maximal L p - L q -estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an {\mathcal{R}} -sectorial operator in L{p}{\sigma}(\Omega), 1 ",

keywords = "Exterior domains, Maximal L - L -estimates, Stokes equation",

author = "Matthias Geissert and Matthias Hess and Hieber, {Matthias Georg} and C{\'e}line Schwarz and Kyriakos Stavrakidis",

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AU - Hess, Matthias

AU - Hieber, Matthias Georg

AU - Schwarz, Céline

AU - Stavrakidis, Kyriakos

PY - 2010/3

Y1 - 2010/3

N2 - Introducing a new localization method involving Bogovskis operator we give a short and new proof for maximal L p - L q -estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an {\mathcal{R}} -sectorial operator in L{p}{\sigma}(\Omega), 1

AB - Introducing a new localization method involving Bogovskis operator we give a short and new proof for maximal L p - L q -estimates for the solution of the Stokes equation. Moreover, it is shown that, up to constants, the Stokes operator is an {\mathcal{R}} -sectorial operator in L{p}{\sigma}(\Omega), 1

KW - Exterior domains

KW - Maximal L - L -estimates

KW - Stokes equation

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ER -

Maximal L p - L q -Estimates for the stokes equation: A short proof of solonnikov's theorem

Abstract

Keywords

ASJC Scopus subject areas

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