Neumann problems for the Stokes equations in convex domains

Jun Geng; Zhongwei Shen

doi:10.1016/j.jfa.2025.111151

Neumann problems for the Stokes equations in convex domains

Jun Geng
, Zhongwei Shen

Mathematics

Producción científica: Article › revisión exhaustiva

Resumen

This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in R^d. We obtain nontangential maximal function estimates in L^p and W^1,p estimates for p in certain ranges depending on d. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a W^2,2 estimate for the Stokes equations in convex domains.

Idioma original	English
Número de artículo	111151
Publicación	Journal of Functional Analysis
Volumen	289
N.º	11
DOI	https://doi.org/10.1016/j.jfa.2025.111151
Estado	Published - dic 1 2025

Nota bibliográfica

Publisher Copyright:
© 2025 Elsevier Inc.

Financiación

Supported in part by NNSF grant 12371096.Supported in part by NSF grant DMS-2153585.

Financiadores	Número del financiador
National Natural Science Foundation of China (NSFC)	12371096
National Science Foundation Arctic Social Science Program	DMS-2153585

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2025.111151

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title = "Neumann problems for the Stokes equations in convex domains",

abstract = "This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in Rd. We obtain nontangential maximal function estimates in Lp and W1,p estimates for p in certain ranges depending on d. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a W2,2 estimate for the Stokes equations in convex domains.",

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author = "Jun Geng and Zhongwei Shen",

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AU - Shen, Zhongwei

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N2 - This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in Rd. We obtain nontangential maximal function estimates in Lp and W1,p estimates for p in certain ranges depending on d. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a W2,2 estimate for the Stokes equations in convex domains.

AB - This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in Rd. We obtain nontangential maximal function estimates in Lp and W1,p estimates for p in certain ranges depending on d. These ranges are larger than the known ranges for Lipschitz domains. The proof relies on a W2,2 estimate for the Stokes equations in convex domains.

KW - Convex domain

KW - Stokes equations

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UR - https://www.scopus.com/pages/publications/105011492302#tab=citedBy

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DO - 10.1016/j.jfa.2025.111151

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JO - Journal of Functional Analysis

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Neumann problems for the Stokes equations in convex domains

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ASJC Scopus subject areas

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