Global Existence and Large Time Behavior for the 2-D Compressible Navier-Stokes Equations without Heat Conductivity

Abstract

In this paper, we consider an initial value problem for the 2-D compressible Navier-Stokes equations without heat conductivity. We prove the global existence of a strong solution when the initial perturbation is small in H2 and its L1 norm is bounded. Moreover, we derive some decay estimate for such a solution.