Very weak solutions of the Stokes problem in a convex polygon

2015/12/02 by Makram Hamouda, Roger Témam, Hamouda, Makram +3
Computer Science · Mathematics · #35D30 #76D03 #76D07 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1512.00898

openalex publication_date 2015/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the study of the corner singularities in the so-called cavity flow, we establish in this article, the existence and uniqueness of solutions in L²(Ω)² for the Stokes problem in a domain Ω, when Ω is a smooth domain or a convex polygon. We establish also a trace theorem and show that the trace of u can be arbitrary in L²(∂Ω)². The results are also extended to the linear evolution Stokes problem.

Related

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• Convergence in the incompressible limit of the corner singularities
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• Axisymmetric Stokes equations in polygonal domains: regularity and finite element approximations
• Lp estimates of solutions to mixed boundary value problems for the Stokes system in polyhedral domains