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

Abstract

This paper is concerned with 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 result on the existence and uniqueness of a globally smooth nonvacuum solution is obtained provided that the $(\gamma-1)\cdot (H^3({\bf R})$-norm of the initial perturbation)$<C$ for some positive constant $C$ independent of $\gamma-1$. Here $\gamma>1$ is the adiabatic gas constant. This is a Nishida--Smoller type global solvability result with large data.