Blow-up Problems Of Smooth Solutions To Cauchy Problem For The Compressible Navier-Stokes Equations

In this paper we are concerned with some blow-up problems of the compressible Navier-Stokes equations. We obtain the blow-up result of the smooth solution to the Cauchy problem for the three-dimensional isothermal Navier-Stokes equations with the help of the energy method.In terms of the function method, we also prove the blow-up result to the Cauchy problem of the isentropic Navier-Stokes equations with the inhomogeneous term.