Global existence of classical solutions to the Cauchy problem for a kind of quasilinear hyperbolic system

This paper deals with the Cauchy problem for a kind of quasilinear hyperbolic system, with the linear elastodynamic system as its principal part and the nonlinear terms depending on quadratic terms of the first derivatives of uu. A system of new null conditions is given, by which the author shows the global existence of the problem.