Remarks on the Well-Posedness of the Nonlinear Cauchy Problem

Guy Metivier (1)

1 IMB - Institut de Mathématiques de Bordeaux

We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of solutions and we analyze Hadamard's instabilities in Sobolev spaces. We also show that genuinely nonlinear equations raise new interesting problems.

Mots clés: Cauchy Problem; well posedness; Hadamard's instability

Domaines: Equations aux dérivées partielles [math.AP]

Guy Metivier. Remarks on the Well-Posedness of the Nonlinear Cauchy Problem. Contemporary mathematics, 2005, 368, pp.337-356. ⟨hal-00113899⟩