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

Chérif Amrouche (1) , M. Meslameni (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

In this article, we solve the Stokes problem in an exterior domain of ℝ3, 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 Wm,2(Ω) when Ω is bounded; see [3, 4]. © 2013 Texas State University-San Marcos.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Chérif Amrouche, M. Meslameni. Stokes problem with several types of boundary conditions in an exterior domain. Electronic Journal of Differential Equations, 2013, 2013, pp.1-28. ⟨hal-00985042⟩