Propagation du front d'onde \(C^ p\) pour des équations non linéaires (Q1821267)

We show propagation results of the \(C^ p\) wave front for a class of paradifferential operators. More precisely, we prove that for ''parafields'' in \({\mathbb{R}}^ n\) (n arbitrary), the \(C^ p\) wave front propagates along the operator's bicharacteristics and can be characterized by the wave front of the trace on a transversal hypersurface. We also prove analogous results for paradifferential operators of order \(m\geq 1\) in the plane \((n=2).\) Using Bony's theory, these results can be applied to non linear partial differential equations.