Stokes problems in irregular domains with various boundary conditions

Sylvie Monniaux; Zhongwei Shen

doi:10.1007/978-3-319-13344-7_4

Stokes problems in irregular domains with various boundary conditions

Sylvie Monniaux, Zhongwei Shen

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

3 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 language	English
Title of host publication	Handbook of Mathematical Analysis in Mechanics of Viscous Fluids
Pages	207-248
Number of pages	42
ISBN (Electronic)	9783319133447
DOIs	https://doi.org/10.1007/978-3-319-13344-7_4
State	Published - Apr 19 2018

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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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10.1007/978-3-319-13344-7_4

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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.",

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ER -

Stokes problems in irregular domains with various boundary conditions

Abstract

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ASJC Scopus subject areas

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