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2015 Improvement of the energy method for strongly nonresonant dispersive equations and applications
Luc Molinet, Stéphane Vento
Anal. PDE 8(6): 1455-1495 (2015). DOI: 10.2140/apde.2015.8.1455

Abstract

We propose a new approach to prove the local well-posedness of the Cauchy problem associated with strongly nonresonant dispersive equations. As an example, we obtain unconditional well-posedness of the Cauchy problem in the energy space for a large class of one-dimensional dispersive equations with a dispersion that is greater than the one of the Benjamin–Ono equation. At the level of dispersion of the Benjamin–Ono, we also prove the well-posedness in the energy space but without unconditional uniqueness. Since we do not use a gauge transform, this enables us in all cases to prove strong convergence results in the energy space for solutions of viscous versions of these equations towards the purely dispersive solutions. Finally, it is worth noting that our method of proof works on the torus as well as on the real line.

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Luc Molinet. Stéphane Vento. "Improvement of the energy method for strongly nonresonant dispersive equations and applications." Anal. PDE 8 (6) 1455 - 1495, 2015. https://doi.org/10.2140/apde.2015.8.1455

Information

Received: 13 January 2015; Revised: 24 April 2015; Accepted: 21 May 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1330.35384
MathSciNet: MR3397003
Digital Object Identifier: 10.2140/apde.2015.8.1455

Subjects:
Primary: 35A02, 35E15, 35Q53

Rights: Copyright © 2015 Mathematical Sciences Publishers

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