Multifrequency NLS scaling for a model equation of gravity-capillary waves

Nader Masmoudi, Kenji Nakanishi

Research output: Contribution to journalArticle

Abstract

This paper is the first in a series papers devoted to the study of the rigorous derivation of the nonlinear Schrödinger (NLS) equation as well as other related systems starting from a model coming from the gravity-capillary water wave system in the long-wave limit. Our main goal is to understand resonances and their effects on having the nonlinear Schrödinger approximation or modification of it or having other models to describe the limit equation. In this first paper, our goal is not to derive NLS but to allow the presence of an arbitrary sequence of frequencies around which we have a modulation and prove local existence on a uniform time. This yields a new class of large data for which we have a large time of existence.

Original languageEnglish (US)
Pages (from-to)1202-1240
Number of pages39
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number8
DOIs
StatePublished - Aug 2013

Fingerprint

Capillary-gravity Waves
Gravitation
Scaling
Nonlinear Approximation
Local Existence
Large Data
Water waves
Water Waves
Nonlinear equations
Gravity
Nonlinear Equations
Modulation
Series
Arbitrary
Model
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Multifrequency NLS scaling for a model equation of gravity-capillary waves. / Masmoudi, Nader; Nakanishi, Kenji.

In: Communications on Pure and Applied Mathematics, Vol. 66, No. 8, 08.2013, p. 1202-1240.

Research output: Contribution to journalArticle

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