Singularity Formation for a System of Conservation Laws in Two Space Dimensions

We study singularity formation for the 2×2 systemu_t+(u²)_x+(uv)_y=0 andv_t+(uv)_x+(v²)_y=0. Our analysis is based on the argument, due to J. Keller and L. Ting (1966,Comm. Pure. Appl. Math.19, 371–420), about the evolution along a characteristic of the compression rate of nearby characteristics. This system is one of a class of systems, called partially aligned, which exhibit a degenerate characteristic structure where a pair of directions replaces the usual cone at every point.