Fundamental solutions for stationary Stokes systems with measurable coefficients

2017/05/08 by Jongkeun Choi, Choi, Jongkeun, Minsuk Yang +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1705.02736

openalex publication_date 2017/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space ℝ^d, d ≥ 3, under the assumption that weak solutions of the system are locally Hölder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on Ω, where Ω is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.

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