One-dimensional Compressible Navier-Stokes Equations with Temperature Dependent Transport Coefficients and Large Data

TL;DR

This paper establishes the existence of global smooth solutions for the one-dimensional compressible Navier-Stokes equations with temperature-dependent transport coefficients and large initial data, extending classical results to more complex, physically realistic models.

Contribution

It proves a Nishida-Smoller type result for large data solutions with temperature-dependent coefficients, which was previously unresolved.

Findings

Global smooth solutions are shown to exist for large initial data.

Temperature-dependent transport coefficients are incorporated into the analysis.

The results extend classical theory to more physically realistic models.

Abstract

This paper is concerned with the global smooth non-vacuum solutions with large data to the Cauchy problem of the one-dimensional compressible Navier-Stokes equations with degenerate temperature dependent transport coefficients which satisfy conditions from the consideration in kinetic theory. A Nishida-Smoller type result is obtained.