Global well-posedness and asymptotic behavior of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients

TL;DR

This paper proves the global existence and decay rates of large strong solutions to the 3D full compressible Navier-Stokes equations with temperature-dependent coefficients, addressing a longstanding challenge in multi-dimensional fluid dynamics.

Contribution

It establishes the first global existence result for large strong solutions with temperature-dependent coefficients in 3D, including optimal decay rates for initial data in certain Lebesgue spaces.

Findings

Global existence of large strong solutions is proven.

Optimal decay rates to equilibrium are established.

Results apply to initial data close to large constant states.

Abstract

It is well known that the global well-posedness of the Navier-Stokes equations with temperature-dependent coefficients is a challenging problem, especially in multi-dimensional space. In this paper, we study the 3D Navier-Stokes equations with temperature-dependent coefficients in the whole space. When the initial density and the initial temperature are linearly equivalent to some large constant states, we establish the first result on the global existence of large strong solution. Moreover, the optimal decay rates of the solution to its associated equilibrium are established when the initial data belong to $L^{p_0}(\mathbb{R}^3)$ for some $p_0\in[1,2]$.