Propagation de la régularité locale de solutions d'équations hyperboliques non linéaires. (Propagation of local smoothness for solutions of nonlinear hyperbolic equations) (Q1821959)

For each positive number s, we study the propagation of local smoothness \(H^ s\) for solutions of nonlinear hyperbolic equations, under assumptions of minimal smoothness allowing to define the nonlinear terms in the equation. In particular, we prove a theorem of propagation in the case of essentially bounded (resp. Lipschitz continuous) solutions of first order semilinear (resp. quasilinear) systems.