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Improvement of the energy method for strongly non resonant dispersive equations and applications

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.
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https://hal.archives-ouvertes.fr/hal-01064252
Contributor : Luc Molinet <>
Submitted on : Monday, September 15, 2014 - 9:54:12 PM
Last modification on : Tuesday, May 5, 2020 - 1:03:21 PM
Document(s) archivé(s) le : Tuesday, December 16, 2014 - 11:46:01 AM

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  • HAL Id : hal-01064252, version 1
  • ARXIV : 1409.4525

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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⟩

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