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

TL;DR

This paper establishes the existence and uniqueness of strong solutions to the stationary exterior Stokes equations with Navier boundary conditions in weighted L^p spaces, advancing understanding of fluid flow in exterior domains.

Contribution

It introduces a framework for analyzing the stationary exterior Stokes problem with Navier boundary conditions in weighted L^p spaces, proving existence and uniqueness of strong solutions.

Findings

Existence of strong solutions in weighted L^p spaces for p > 2

Uniqueness of solutions under Navier boundary conditions

Characterization of solution behavior at infinity

Abstract

This paper treats the stationary Stokes problem in exterior domain of $\mathbb{R}^3$ with Navier slip boundary condition. The behavior at infinity of the data and the solution are determined by setting the problem in $L^p$-spaces, for $p> 2$, with weights. The main results are the existence and uniqueness of strong solutions of the corresponding system.