Séminaire MACS (Modélisation, Analyse et Calcul Scientifique). Commun ICJ & UMPA.

Long time existence results for the abcd Boussinesq systems

par Cosmin Burtea (Université Claude Bernard Lyon 1)

Europe/Paris
salle Fokko du Cloux (ICJ, UCBL - La Doua, Bât. Braconnier)

salle Fokko du Cloux

ICJ, UCBL - La Doua, Bât. Braconnier

Description
The abcd systems were derived by J.B. Bona, M. Chen and J.-C. Saut in 2002 as approximation models in order to study the propagation of small amplitude, long wavelength water waves in a channel with flat bottom. First, we will recall the formal derivation of these models. We will see that observations of practical order lead to the conclusion that in order to be physically relevant, solutions of the Cauchy problem associated to these systems need to exist on times which are of the same order as the ratio between the depth of the channel and a typical amplitude (which in this case is supposed to be large). Thus, in a second time, we will present such results, referred in the literature as long time existence results, that we obtain for both spatially localized respectively non-localized initial data.