Exterior Navier-Stokes flows for bounded data

TL;DR

This paper establishes the unique existence of mild solutions to the Navier-Stokes equations in exterior domains with bounded initial data, advancing understanding of fluid flows around obstacles.

Contribution

It proves the existence and uniqueness of solutions in exterior domains for bounded initial data, extending previous results to more general settings.

Findings

Unique existence of mild solutions in exterior domains

Solutions are valid for bounded initial data in $L^{ abla}_{ ext{bounded}}$

Addresses non-slip boundary conditions in fluid flow models

Abstract

We prove unique existence of mild solutions on $L^{\infty}_{\sigma}$ for the Navier-Stokes equations in an exterior domain in $ \mathbb{R}^{n}$, $n\geq 2$, subject to the non-slip boundary condition.