Global well-posedness of non-heat conductive compressible Navier–Stokes equations in 1D

Abstract

In this paper, the initial-boundary value problem of the one-dimensional full compressible Navier–Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any H1 initial data. The initial density is assumed only to be nonnegative, and, thus, is not necessary to be uniformly away from vacuum. Comparing with the well-known result of Kazhikhov and Shelukhin (1977 J. Appl. Math. Mech. 41 273–282), the heat conductive coefficient is zero in this paper, and the initial vacuum is allowed.