Strichartz estimates for wave equations with coefficients of Sobolev regularity

Abstract

Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. In this work, such methods are used to show Strichartz inequalities for wave equations with coefficients lying in an Lr Sobolev space of order strictly greater than n-1r + 2, n denoting the dimension of the spatial variables. In addition, a weaker family of weighted Strichartz type estimates are developed for wave equations with coefficients in an Lr Sobolev space of order n-1r + 1+ alpha, where 0 < alpha < 1.