Global classical solutions to the Cauchy problem for a nonlinear wave equation

Abstract

In this paper we consider the Cauchy problem {u″+M(|A12u|2)Au=0   in   ]0,T[u(0)=u0,       u′(0)=u1, where u′ is the derivative in the sense of distributions and |A12u| is the H-norm of A12u. We prove the existence and uniqueness of global classical solution.