Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data

TL;DR

This paper establishes the global existence and uniqueness of solutions to the 2D exterior Navier-Stokes equations with bounded initial data, including large Reynolds numbers, expanding understanding of fluid flow in unbounded domains.

Contribution

It proves global well-posedness for 2D exterior Navier-Stokes with non-decaying data and constructs solutions for large Reynolds numbers and asymptotically constant initial conditions.

Findings

Global solutions exist for bounded initial data with finite Dirichlet integral.

Solutions are valid for arbitrarily large Reynolds numbers.

Constructs solutions for asymptotically constant initial data.

Abstract

We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions for asymptotically constant initial data and arbitrary large Reynolds numbers.