Resolvent estimates for the Stokes operator in bounded and exterior C1 domains

Jun Geng; Zhongwei Shen

doi:10.1007/s00208-024-02956-z

Resolvent estimates for the Stokes operator in bounded and exterior C1 domains

Jun Geng, Zhongwei Shen

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

2 Scopus citations

Abstract

We establish resolvent estimates in L^q spaces for the Stokes operator in a bounded C¹ domain Ω in R^d. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in L^q(Ω;C^d) for any 1<q<∞ and d≥2. The case of an exterior C¹ domain is also studied.

Original language	English
Pages (from-to)	1467-1503
Number of pages	37
Journal	Mathematische Annalen
Volume	391
Issue number	1
DOIs	https://doi.org/10.1007/s00208-024-02956-z
State	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

Funding

Jun Geng: Supported in part by NNSF grant 12371096. Zhongwei Shen: Supported in part by NSF grant DMS-2153585.

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-2153585, 2153585
National Natural Science Foundation of China (NSFC)	12371096

ASJC Scopus subject areas

General Mathematics

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abstract = "We establish resolvent estimates in Lq spaces for the Stokes operator in a bounded C1 domain Ω in Rd. As a corollary, it follows that the Stokes operator generates a bounded analytic semigroup in Lq(Ω;Cd) for any 11 domain is also studied.",

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Resolvent estimates for the Stokes operator in bounded and exterior C1 domains

Abstract

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