$L^p$-theory for the exterior Stokes problem with Navier's type slip-without-friction boundary conditions

TL;DR

This paper develops an $L^p$-theory for the stationary exterior Stokes problem with slip boundary conditions, establishing existence and uniqueness of weak solutions in weighted Sobolev spaces for $p>3$.

Contribution

It introduces a novel $L^p$-framework for the exterior Stokes problem with slip boundary conditions, focusing on existence and uniqueness in weighted Sobolev spaces.

Findings

Established inf-sup conditions crucial for analysis.

Proved existence and uniqueness of weak solutions for $p>3$.

Extended the $L^p$-theory to exterior domains with slip boundary conditions.

Abstract

In this paper, we consider the stationary Stokes equations in an exterior domain three-dimensional under a slip boundary condition without friction. We set the problem in weighted Sobolev spaces in order to control the behavior at infinity of the solutions. In this work, we try to investigate the existence and uniqueness of the weak solutions related to this problem in $L^P-$theory when $p>3$. Our proof are based on obtaining inf-sup conditions that play a fundamental role.