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

3 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
National Science Foundation Arctic Social Science Program	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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AB - 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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