The initial value problem for the compressible Navier-Stokes equations without heat conductivity

Abstract(#br)In this paper, we are concerned with the global existence and convergence rates of strong solutions for the compressible Navier-Stokes equations without heat conductivity in R 3 . The global existence and uniqueness of strong solutions are established by the delicate energy method under the condition that the initial data are close to the constant equilibrium state in H 2 -framework. Furthermore, if additionally the initial data belong to L 1 , the optimal convergence rates of the solutions in L 2 -norm and convergence rates of their spatial derivatives in L 2 -norm are obtained