A Liouville theorem for the Degasperis-Procesi equation

Lorenzo Brandolese (1)

1 ICJ - Institut Camille Jordan

We prove that the only global, strong, spatially periodic solution to the Degasperis-Procesi equation, vanishing at some point $(t_0,x_0)$, is the identically zero solution. We also establish the analogue of such Liouville-type theorem for the Degasperis-Procesi equation with an additional dispersive term.

Mots clés: Wave breaking; Bloup; Nonlinear dispersive waves; Shallow water; Integrable systems

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brandolese. A Liouville theorem for the Degasperis-Procesi equation. 2014. ⟨hal-00996383v1⟩