Blow-up for the b-family of equations

Manuel Fernando Cortez Estrella (1)

1 EDPA - Équations aux dérivées partielles, analyse

In this paper we consider the $b$-family of equations on the torus $u_t- u_{txx}+ (b+1) u u_x=b u_x u_{xx} + u u_{xxx}$, which for appropriate values of $b$ reduces to well-known models, such as the Camassa-Holm equation or the Degasperis-Procesi equation. We establish a local-in-space blow-up criterion

Mots clés: Degasperis -Procesi.; Blow up local criterion; B-Family of Equations; Camassa Holm; Degasperis -Procesi; Local-in-space criteria for blow-up

Domaines: Equations aux dérivées partielles [math.AP]

Manuel Fernando Cortez Estrella. Blow-up for the b-family of equations. 2014. ⟨hal-01024158v3⟩