Global solutions to systems of quasilinear wave equations with low regularity data and applications

Abstract

In this paper, we study the Cauchy problem for systems of 3-D quasilinear wave equations satisfying the null condition with initial data of low regularity. In the radially symmetric case, we prove the global existence for every small data in H3×H2 with a low weight. To achieve this goal, we will show how to extend the global iteration method first suggested by Li and Chen (1988) [32] to the low regularity case, which is also another purpose of this paper. Finally, we apply our result to 3-D nonlinear elastic waves.