Global existence and convergence rates for the 3-D compressible Navier-Stokes equations without heat conductivity Renjun DuanHongfang Ma 35Q3065M1293D20Navier-Stokes equationsa priori estimateconvergence rates We study the global existence and convergence rates of solutions to the three-dimensional compressible Navier-Stokes equations without heat conductivity, which is a hyperbolic-parabolic system. The pressure and velocity are dissipative because of the viscosity, whereas the entropy is non-dissipative due to the absence of heat conductivity. The global solutions are obtained by combining the local existence and a priori estimates if $H^3$-norm of the initial perturbation around a constant state is small enough and its $L^1$-norm is bounded. A priori decay-in-time estimates on the pressure and velocity are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3326 10.1512/iumj.2008.57.3326 en Indiana Univ. Math. J. 57 (2008) 2299 - 2320 state-of-the-art mathematics http://iumj.org/access/