Global Gevrey solution of 3D anisotropic Navier-Stokes system in a strip domain

TL;DR

This paper proves the global existence of Gevrey-class solutions for a 3D anisotropic Navier-Stokes system in a strip domain, demonstrating regularization effects despite boundary challenges and partial dissipation.

Contribution

It introduces a novel approach using Gevrey regularity in the vertical direction to establish global solutions for anisotropic Navier-Stokes equations with boundary effects.

Findings

Solutions exhibit space-time Gevrey regularity in horizontal directions.

Vertical Gevrey regularity is imposed to handle boundary difficulties.

Enhanced regularity is achieved in the strongly diffusive direction.

Abstract

We investigate the three-dimensional (3D) incompressible anisotropic Navier-Stokes system with dissipation only in the horizontal variables, posed in a strip domain. To overcome the difficulties arising from the boundary terms and the absence of vertical dissipation, we impose a Gevrey-class regularity condition in the vertical direction. For the remaining directions, we prove that the solution exhibits space-time analytic or Gevrey-class regularization. Furthermore, the solution is shown to possess an enhanced Gevrey regularity in the direction of strong diffusion, which is unconstrained by boundaries.