Global large strong solution of the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity

TL;DR

This paper proves the existence of a unique global strong solution for the 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity, even for large initial data, marking a significant advancement in the field.

Contribution

It establishes the first result on large strong solutions for 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity.

Findings

Existence of unique global strong solutions for large initial data

First such result for 3D inhomogeneous Navier-Stokes with density-dependent viscosity

Solution existence under power-law viscosity coefficient

Abstract

This paper concerns the Dirichlet problem of three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity. When the viscosity coefficient $\mu(\rho)$ is a power function of the density ($\mu(\rho)=\mu\rho^\alpha$ with $\alpha>1$), it is proved that the system will admit a unique global strong solution as long as the initial data are sufficiently large. This is the first result concerning the existence of large strong solution for the inhomogeneous Navier-Stokes equations in three dimensions.