Séminaire d'analyse

Local well-posedness for the gKdV equation on the background of a bounded function.

par M. José Palacios (Université de Tours)

Europe/Paris
E1 2040 (Tours)

E1 2040

Tours

Description

In this talk we will prove the LWP for the gKdV equation in Hs(ℝ), s>1/2, under general assumptions on the nonlinearity f(x), on the background of a bounded function Ψ(t,x), with Ψ(t,x) satisfying some suitable conditions. As a consequence of our estimates, we also obtain the unconditional uniqueness of the solution in Hs(ℝ). This result not only gives us a framework to solve the gKdV equation around a Kink, for example, but also around a periodic solution, that is, to consider localized non-periodic perturbations of a periodic solution.