On the two-dimensional Navier-Stokes equations with horizontal viscosity

Abstract

This paper is concerned with a 2D channel flow that is periodic horizontally but bounded above and below by hard walls. We assume the presence of horizontal viscosity only. We study the well-posedness, large-time behavior, and stability of solutions. For global well-posedness, we aim to assume less differentiability on initial velocity $(u_0,v_0)$: in particular, we assume $u_0,v_0\in L^2(\hat{I}\text{c◯})$ and ${\partial }_y{u}_0\in L^2(\hat{I}\text{c◯})$.