The Cauchy problem for one-dimensional flow of a compressible viscous fluid: stabilization of the solution

Abstract

We analyze the Cauchy problem for non-stationary 1-D flow of a compressible viscous and heat-conducting fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on R×]0, T [ for each T > 0. Supposing that the initial functions are small perturbations of the constants and using some a priori estimates for the solution independent of T , we prove a stabilization of the solution.