Global existence for systems of nonlinear wave equations in two space dimensions
The author considers the Cauchy problem for a system of fully nonlinear wave equations of the type \[ \square u_i = F_i (u,u',u'') \text{ in } \overline \mathbb{R}_+\times\mathbb{R}^n, \quad u_i (0,x) = \varepsilon f_i (x),\;\partial_t u_i (0,x) = \varepsilon g_i (x),\;x \in \mathbb{R}^n \] where \(n = 2\), and \(F = O (|u |^p + |u' |^p + |u'' |^p)\) with \(p = 3\). He proves the global existence of the classical solution under certain assumptions, following the method given in Klainerman's previous paper.
scientific article; zbMATH DE number 562836
scientific article