On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

Takayuki Abe, Masao Yamazaki

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow.

Original languageEnglish
Pages (from-to)61-100
Number of pages40
JournalJournal of Mathematical Fluid Mechanics
Volume12
Issue number1
DOIs
Publication statusPublished - 2010 Mar 1

Keywords

  • Besov space
  • Homogeneous Besov space
  • Infinite layer
  • Poiseuille flow
  • Sobolev space
  • Stationary problem
  • Stokes equation

ASJC Scopus subject areas

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

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