Global existence for systems of quasilinear wave equations in (1 + 4)-dimensions (Q2285476)

The authors consider the Cauchy problem and exterior domain problem for multiple-speeds systems of quasilinear wave equations in four space dimensions. They show that, if the nonlinerity does not contain the quadaratic terms of the solution itself, then the classical solution must be global for small initial data. Such result was first established by Hörmander for the Cauchy problem of scalar wave equations. But the method cannot be applied to the case of multiple-speeds system. The authors develop some robust approach to extend Hörmander's result to this case.