Gradient estimates for Stokes and Navier-Stokes systems with piecewise DMO coefficients

2021/05/12 by Jongkeun Choi, Hongjie Dong, Choi, Jongkeun +3
Computer Science · Engineering · Mathematics · #35B65 #35J47 #76D07 #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.2105.05429

openalex publication_date 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study stationary Stokes systems in divergence form with piecewise Dini mean oscillation coefficients and data in a bounded domain containing a finite number of subdomains with C^1,\rmDini boundaries. We prove that if (u, p) is a weak solution of the system, then (Du, p) is bounded and piecewise continuous. The corresponding results for stationary Navier-Stokes systems are also established, from which the Lipschitz regularity of the stationary H¹-weak solution in dimensions d=2,3,4 is obtained.

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