Global small amplitude solutions to systems of nonlinear wave equations with multiple speeds

We give a global existence theorem to systems of quasilinear wave equations in three space dimensions, especially for the multiple-speed cases. It covers a wide class of quadratic nonlinearities which may depend on unknowns as well as their first and second derivatives. Our proof is achieved through total use of pointwise and L-2-estimates concerning unknowns and their first and second derivatives.