On the three-dimensional stationary exterior Stokes problem with Non Standard Boundary Conditions

Héla Louati (1, 2) , Mohamed Meslameni (2, 1) , Ulrich Razafison (3)

1 Université de Sfax - University of Sfax
2 Al-Baha University
3 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

We study the three-dimensional stationary exterior Stokes problem with non standard boundary conditions corresponding to a slip-without-friction boundary conditions. Because the flow domain is unbounded , we set the problem in weighted spaces in order to control the behavior at infinity of solutions. This functional framework allows to prescribe various behaviors at infinity of the solutions. The results established are related to the existence and the uniqueness of strong and very weak solutions. Our strategy relies on the fact that due to the boundary conditions, the pressure and the velocity can be decoupled and, as a result, we solve two separate systems to find these quantities.

Mots clés: Fluid mechanics; Stokes equations; Slip boundary conditions; Exterior domains; Strong solutions; Very weak solutions; Weighted spaces

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Héla Louati, Mohamed Meslameni, Ulrich Razafison. On the three-dimensional stationary exterior Stokes problem with Non Standard Boundary Conditions. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2020, 100 (6), ⟨10.1002/zamm.201900181⟩. ⟨hal-02174108v2⟩