Some results on blowup of solutions for the compressible Navier-Stokes equations

In this thesis, the author study the blowup of solutions for strong and classical solutions to the compressible Navier-Stokes equations. In the first part, we prove a blow up criterion for strong solutions to the compressible Navier-Stokes equations, similar to the Beal-Kato-Majda criterion for the ideal incompressible flows.;The same criterion for classical solutions to the compressible Navier-Stokes equations is established in the second part of this thesis. In addition, initial vacuum is allowed in both cases.;Finally, we prove a blow up criterion for the full compressible Navier-Stokes equations just in terms of the gradient of the velocity.