THE CAUCHY PROBLEM FOR THE \Bfitn-Dimensional COMPRESSIBLE NAVIER-STOKES EQUATIONS WITHOUT HEAT CONDUCTIVITY

The global existence and convergence rates of solutions to the three-dimensional compressible Navier-Stokes equations without heat conductivity have been obtained since Duan and the global small solutions to the compressible Navier--Stokes equations without heat conductivity in R2 is still an open problem. In the present paper, we give a positive answer in Rn (n = 2,3) with the initial data restricted in the Besov spaces.