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

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• $L^p$-Strong solution for the stationary exterior Stokes equations with Navier boundary condition