Global existence for some 4-D quasilinear wave equations with low regularity

Abstract

In this paper, we prove the global existence for some 4-D quasilinear wave equations with small, radial data in $H^3\times H^2$. The main idea is to exploit local energy estimates with variable coefficients, together with the trace estimates.

12 pages, to appear in Acta Mathematica Sinica, English Series