Abstract : In this paper we propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly non resonant dispersive equations. As an example we obtain unconditional well-posedness of the Cauchy problem below $ H^1 $ for a large class of one-dimensional dispersive equations with a dispersion that is greater or equal to the one of the Benjamin-Ono equation. Since this is done without using a gauge transform, this enables us to prove strong convergence results for solutions of viscous versions of these equations towards the purely dispersive solutions.
https://hal.archives-ouvertes.fr/hal-01064252
Contributeur : Luc Molinet
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Soumis le : lundi 15 septembre 2014 - 21:54:12
Dernière modification le : jeudi 7 février 2019 - 17:52:48
Document(s) archivé(s) le : mardi 16 décembre 2014 - 11:46:01
Luc Molinet, Stéphane Vento. Improvement of the energy method for strongly non resonant dispersive equations and applications. Analysis & PDE, Mathematical Sciences Publishers, 2015, 8 (6), pp.1455-1495. 〈hal-01064252〉
