| In this thesis, the author studies the global existence and the large time behavior of strong and classical solutions to the Navier-Stokes equations for viscous compressible fluids.; First, he proves that for the two dimensional Stokes approximation equations for the compressible flows together with the space-periodicity boundary condition or the no-stick boundary condition or Cauchy problem, there exists a unique global strong solution or a unique global classical solution for arbitrarily large initial data; moreover, it is shown that the density is bounded from above independent of time. For the three dimensional flows, if the initial data are small enough, the same results hold true.; Second, he shows that for the space-periodicity boundary condition or the nostick boundary condition, if the initial density contains vacuum at least at one point, then the global strong (or classical) solution obtained in the first step for the Stokes approximation equations for the compressible flows must blow up as time goes to infinity.; Finally, as an application, it is also shown that if the initial density contains vacuum at least at one point, then the strong solution to the initial-boundary-value problem for the 1D Navier-Stokes equations for a compressible fluid for the barotropic motion with the Dirichlet boundary condition has to blow up as time goes to infinity. |
