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

We study singularity formation for the 2=2 system utq u2.xq u¨.ys0 and ¨tq u¨.xq ¨2.ys0. 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.