Fundamental solutions for stationary Stokes systems with measurable coefficients

Jongkeun Choi, Minsuk Yang

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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 Rd, 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.

Original languageEnglish
Pages (from-to)3854-3893
Number of pages40
JournalJournal of Differential Equations
Volume263
Issue number7
DOIs
Publication statusPublished - 2017 Oct 5

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All Science Journal Classification (ASJC) codes

  • Analysis

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