On the global existence and stability of 3-D viscous cylindrical circulatory flows

TL;DR

This paper proves the global existence and stability of 3-D viscous circulatory flows around an infinite cylinder using energy estimates, demonstrating stability under small initial perturbations.

Contribution

It introduces weighted energy spaces and a priori estimates to establish the global stability of 3-D cylindrical circulatory flows, a novel approach for this problem.

Findings

Global stability of 3-D viscous circulatory flows established

Flow remains stable under small initial perturbations

Method involves weighted energy spaces and a priori estimates

Abstract

In this paper, we are concerned with the global existence and stability of a 3-D perturbed viscous circulatory flow around an infinite long cylinder. This flow is described by 3-D compressible Navier-Stokes equations. By introducing some suitably weighted energy spaces and establishing a priori estimates, we show that the 3-D cylindrical symmetric circulatory flow is globally stable in time when the corresponding initial states are perturbed suitably small.