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.

References in corpus (1)

• Global well-posedness of the KP-I initial-value problem in the energy space

Cited by in corpus (6)

• Low regularity well-posedness for generalized Benjamin-Ono equations on the circle
• On shorttime bilinear Strichartz estimates and applications to improve the energy method
• Deep-water and shallow-water limits of the intermediate long wave equation
• Local and global well-posedness of dispersion generalized Benjamin-Ono equations on the circle
• Local Well-Posedness for the Zakharov System in Dimension $d⩽3$
• Unconditional deep-water limit of the intermediate long wave equation in low-regularity