Partial boundary regularity for the Navier-Stokes equations in time-dependent domains

2023/05/04 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.2305.02602

openalex publication_date 2023/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the incompressible Navier-Stokes equations in a moving domain whose boundary is prescribed by a function η=η(t,y) (with y∈\mathbb R2) of low regularity. This is motivated by problems from fluid-structure interaction. We prove partial boundary regularity for boundary suitable weak solutions assuming that η is continuous in time with values in the fractional Sobolev space W2-1/p,py for some p>15/4 and we have ∂tη∈ Lt3(W1,q0y) for some q0>2. The existence of boundary suitable weak solutions is a consequence of a new maximal regularity result for the Stokes equations in moving domains which is of independent interest.

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