GLOBAL EXISTENCE OF SOLUTIONS FOR ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS

We present global existence results for weak solutions of isentropic, compressible Navier-Stokes equations in arbitrary dimensions (N greater-than-or-equal-to 2) with arbitrary initial data (finite mass and total energy). In the case of a pressure law p(rho) = alpha rho(y) (a > 0), the result is shown under the condition gamma greater-than-or-equal-to gamma0(N) with gamma0(2) = 3/2 for example. The proof relies upon ''stability'' properties of sequences of solutions and on appropriate approximations based upon, for instance, the study of stationary problems. And we give, for these stationary problems, existence results of weak solutions and regularity results if N=2 or if N=3.