Green Functions of Conormal Derivative Problems for Stationary Stokes System

Jongkeun Choi, Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the Stokes system are continuous in the interior of the domain. Also, we establish the global pointwise bound for the Green function under the additional assumption that weak solutions of the conormal derivative problem for the Stokes system are locally bounded up to the boundary. We provide some examples satisfying such continuity and boundedness properties.

Original languageEnglish
Pages (from-to)1745-1769
Number of pages25
JournalJournal of Mathematical Fluid Mechanics
Volume20
Issue number4
DOIs
Publication statusPublished - 2018 Dec 1

Keywords

  • Conormal derivative problem
  • Green function
  • Measurable coefficients
  • Stokes system

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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