Archive for Rational Mechanics and Analysis

, Volume 114, Issue 4, pp 313–333

A well-posed problem for the exterior Stokes equations in two and three dimensions

Authors

  • Vivette Girault
    • Laboratoire d'Analyse Numérique Tour 55-655ème étage Université Pierre et Marie Curie
    • INIC/CMAF Universidade de Lisboa
  • Adelia Sequeira
    • Laboratoire d'Analyse Numérique Tour 55-655ème étage Université Pierre et Marie Curie
    • INIC/CMAF Universidade de Lisboa
Article

DOI: 10.1007/BF00376137

Cite this article as:
Girault, V. & Sequeira, A. Arch. Rational Mech. Anal. (1991) 114: 313. doi:10.1007/BF00376137

Abstract

This paper treats the Stokes problem in exterior Lipschitz-continuous domains of ℝ2 and ℝ3. Using the weighted Sobolev spaces of Hanouzet (in ℝ3) and Giroire (in ℝ2), we establish the inf-sup condition between the velocity and pressure spaces. This fundamental result shows that the variational Stokes problem is well-posed in those spaces. In the last paragraph, we obtain additional regularity of the solution when the data are smoother.

Copyright information

© Springer-Verlag 1991