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

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)$ 1$ is the adiabatic gas constant. This is a Nishida--Smoller type global solvability result with large data.

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