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

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

Abstract

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.

Original language	English
Article number	111151
Journal	Journal of Functional Analysis
Volume	289
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2025.111151
State	Published - Dec 1 2025

Bibliographical note

Publisher Copyright:
© 2025 Elsevier Inc.

Funding

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

Funders	Funder number
National Natural Science Foundation of China (NSFC)	12371096
National Science Foundation Arctic Social Science Program	DMS-2153585

Keywords

Convex domain
Stokes equations

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2025.111151

Cite this

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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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AU - Shen, Zhongwei

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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.

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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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VL - 289

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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Neumann problems for the Stokes equations in convex domains

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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