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

By Luc Molinet, Stéphane Vento. 2014

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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.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5f175bb16d44e97005e9d8be58d69db8e5b4f0fd