Anisotropic Navier-Stokes equations in a bounded cylindrical domain

TL;DR

This paper investigates the existence and uniqueness of solutions to anisotropic Navier-Stokes equations within a bounded cylindrical domain, focusing on boundary conditions and anisotropic viscosity effects.

Contribution

It provides new results on the global and local well-posedness of anisotropic Navier-Stokes equations in cylindrical geometries with specific boundary conditions.

Findings

Established conditions for existence and uniqueness of solutions

Analyzed effects of anisotropic viscosity on solution behavior

Extended results to bounded cylindrical domains

Abstract

We study the global and local existence and uniqueness of solutions to the Navier-Stokes equations with anisotropic viscosity in a bounded cylindrical domain $Q=\Omega\times (0,1)$, where $\Omega$ is a star-shaped domain in $R^2$. In this paper, we consider the case of homogeneous Dirichlet boundary conditions on the lateral boundary and vanishing normal trace on the top and the bottom.