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 (-1) (H³ (R) -norm of the initial perturbation) 1 is the adiabatic gas constant. This is a Nishida--Smoller type global solvability result with large data.