A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations

摘要

In this paper, we obtain a blow up criterion for classical solutions to the3-D compressible Naiver-Stokes equations just in terms of the gradient of thevelocity, similar to the Beal-Kato-Majda criterion for the ideal incompressibleflow. In addition, initial vacuum is allowed in our case.