Stokes problems in irregular domains with various boundary conditions

Sylvie Monniaux, Zhongwei Shen

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

2 Scopus citations

Abstract

Different boundary conditions for the Navier-Stokes equations in bounded Lipschitz domains in R 3 , such as Dirichlet, Neumann, Hodge, or Robin boundary conditions, are presented here. The situation is a little different from the case of smooth domains. The analysis of the problem involves a good comprehension of the behavior near the boundary. The linear Stokes operator associated to the various boundary conditions is first studied. Then a classical fixed-point theorem is used to show how the properties of the operator lead to local solutions or global solutions for small initial data.

Original languageEnglish
Title of host publicationHandbook of Mathematical Analysis in Mechanics of Viscous Fluids
Pages207-248
Number of pages42
ISBN (Electronic)9783319133447
DOIs
StatePublished - Apr 19 2018

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy
  • General Engineering

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