Resolvent Estimates in L p for the Stokes Operator in Lipschitz Domains

Zhongwei Shen

doi:10.1007/s00205-012-0506-7

Resolvent Estimates in L ^p for the Stokes Operator in Lipschitz Domains

Zhongwei Shen

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

43 Scopus citations

Abstract

We establish the L ^p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ ^d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L ^p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).

Original language	English
Pages (from-to)	395-424
Number of pages	30
Journal	Archive for Rational Mechanics and Analysis
Volume	205
Issue number	2
DOIs	https://doi.org/10.1007/s00205-012-0506-7
State	Published - Aug 2012

Bibliographical note

Funding Information:
Supported in part by NSF grant DMS-0855294.

Funding

Supported in part by NSF grant DMS-0855294.

Funders	Funder number
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	DMS-0855294

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Access to Document

10.1007/s00205-012-0506-7

Cite this

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abstract = "We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ d, d ≥ 3 for \{pipe\}1/p-1/2\{pipe\} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).",

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AB - We establish the L p resolvent estimates for the Stokes operator in Lipschitz domains in ℝ d, d ≥ 3 for {pipe}1/p-1/2{pipe} < 1/2d + εThe result implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in L p for (3/2) - ε < p < 3 + ε. This gives an affirmative answer to a conjecture of M. Taylor (Progr. Nonlinear Differential Equations Appl., vol. 42, pp. 320-334).

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