Uniform estimates in the velocity at infinity for stationary solutions to the Navier-Stokes exterior problem

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Abstract

This paper is concerned with the stationary Navier-Stokes equations in exterior domains of dimension n ≥ 3, and provides a sufficient condition on the external force for the unique solvability. This condition is valid both in the case with small but nonzero velocity at infinity, and in the case with zero velocity at infinity. As a result it is proved that, if the external force satisfies this condition, the solution with nonzero velocity at infinity converges to the solution with zero velocity at infinity with respect to the weak-∗ topology of appropriate function spaces.

Original languageEnglish
Pages (from-to)225-279
Number of pages55
JournalJapanese Journal of Mathematics
Volume31
Issue number2
DOIs
Publication statusPublished - 2005

Keywords

  • Lorentz spaces
  • Navier-Stokes equation
  • Oseen equation

ASJC Scopus subject areas

  • Mathematics(all)

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