Singularity Formation for Radially Symmetric Expanding Wave of Compressible Euler Equations.

In this paper, for compressible Euler equations in multiple space dimensions, we prove the breakdown of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including compression. The singularity formation considered in this paper is corresponding to the finite time shock formation. We also provide some new global sup-norm estimates on velocity and density functions for classical solutions and construct the corre-sponding classical solutions. All results in this paper have no restriction on the size of solutions and hence are large data results.