Stokes problem with several types of boundary conditions in an exterior domain

Abstract

In this article, we solve the Stokes problem in an exterior domain of $\mathbb{R}^{3}$, with non-standard boundary conditions. Our approach uses weighted Sobolev spaces to prove the existence, uniqueness of weak and strong solutions. This work is based on the vector potentials studied in [7] for exterior domains, and in [1] for bounded domains. This problem is well known in the classical Sobolev spaces $ W ^{m,2}(\Omega)$ when $\Omega$ is bounded; see [3,4].

Keywords

• Stokes equations
• exterior domain
• weighted Sobolev spaces
• vector potentials
• inf-sup conditions