Asymptotic stability of small Oseen-type vortex under three-dimensional large perturbation

Abstract

AbstractWe consider the three-dimensional Navier–Stokes equations whose initial data may have infinite kinetic energy. We establish unique existence of the mild solution to the Navier–Stokes equations for small initial data in the whole space{\mathbb{R}^{3}}and a vertically periodic product space{\mathbb{R}^{2}\times\mathbb{T}^{1}}which may be constant in vertical direction so that it includes the Oseen vortex. We further discuss its asymptotic stability under arbitrarily large three-dimensional perturbation in{\mathbb{R}^{2}\times\mathbb{T}^{1}}.