On the blow up criterion for the 2-D compressible Navier-Stokes equations

Motivated by [10], we prove that the upper bound of the density function j9 controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.