Global existence for 1D, compressible, isentropic Navier-Stokes equations with large initial data

Source abstract

We prove the global existence of weak solutions of the Cauchy problem for the Navier-Stokes equations of compressible, isentropic flow of a polytropic gas in one space dimension. The initial velocity and density are assumed to be in L 2 {L^2} and L 2 ∩ B V {L^2} \cap BV respectively, modulo additive constants. In particular, no smallness assumptions are made about the intial data. In addition, we prove a result concerning the asymptotic decay of discontinuities in the solution when the adiabatic constant exceeds 3 / 2 3/2 .