On higher regularity of Stokes systems with piecewise Hölder continuous coefficients

2023/09/13 by Hongjie Dong, Haigang Li, Dong, Hongjie +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Enhanced Oil Recovery Techniques #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2309.06722

openalex publication_date 2023/09/13 · openalex created_date 2023/09/15 · openalex updated_date 2026/08/01

Abstract

In this paper, we consider higher regularity of a weak solution (\bf u,p) to stationary Stokes systems with variable coefficients. Under the assumptions that coefficients and data are piecewise C^s,δ in a bounded domain consisting of a finite number of subdomains with interfacial boundaries in C^s+1,μ, where s is a positive integer, δ∈ (0,1), and μ∈ (0,1], we show that D\bf u and p are piecewise C^s,δ_μ, where δ_μ=min\(1)/(2),μ,δ\. Our result is new even in the 2D case with piecewise constant coefficients.

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