Global well-posedness to the three-dimensional compressible Navier–Stokes equations with anisotropic viscous stress tensor

Abstract

This paper addresses the Cauchy problem for the three-dimensional Navier–Stokes equations with anisotropic viscosity tensor. Under the condition that the initial energy is small enough, we establish the global existence and uniqueness of classical solutions and derive some decay rates. Notably, we extend the results for small energy solutions with isotropic viscous stress tensors originally established by Huang et al., (2012) to the anisotropic case.