Partial boundary regularity for the Navier-Stokes equations in irregular domains

2022/07/31 by Dominic Breit, Breit, Dominic · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.00415

openalex publication_date 2022/07/31 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We prove partial regularity of suitable weak solutions to the Navier--Stokes equations at the boundary in irregular domains. In particular, we provide a criterion which yields continuity of the velocity field in a boundary point and obtain solutions which are continuous in a.a. boundary boundary point (their existence is a consequence of a new maximal regularity result for the Stokes equations in domains with minimal regularity). We suppose that we have a Lipschitz boundary with locally small Lipschitz constant which belongs to the fractional Sobolev space W^2-1/p,p for some p>(15)/(4). The same result was previously only known under the much stronger assumption of a C²-boundary.

Cited by

• On well-posedness theory of very weak solutions to Navier-Stokes equations on irregular domains with nonhomogeneous Dirichlet boundary data

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