PROPAGATION OF SINGULARITIES FOR SEMI-LINEAR WAVE EQUATIONS WITH NONLINEARITY SATISFYING THE NULL CONDITION

Abstract

We study the propagation of singularities for semi-linear wave equations □u = F(u, Du) satisfying the null condition, and improve an earlier result of ours. Microlocal Sobolev regularity in [Formula: see text] propagates along null bicharacteristics, when a suitable condition is imposed on s and r. We provide here optimal conditions on s and r, and improve existing results to include values up to n/2 < s ≦ r < 3s - n when the nonlinearity F(u, Du) satisfies the null condition.