Abstract

We consider the Cauchy problem for systems of semi-linear wave equations with multiple propagation speeds in two space dimensions with small, smooth, and compactly supported data. We assume that the nonlinear terms are cubic and depend only on first derivatives of the unknowns. This is the critical situation, and the null condition (for the single-speed and the multiple-speed cases) is known to be sufficient for the small data global existence. We introduce a weaker sufficient condition for the small data global existence. With some (technical) additional assumptions we also obtain the asymptotic behavior of global solutions. This talk is based on a joint work with Dr. Minggang Cheng.