Bilinear Dispersive Estimates Via Space Time Resonances, Dimensions Two and Three

Frédéric Bernicot, Pierre Germain

Research output: Contribution to journalArticle

Abstract

Consider a bilinear interaction between two linear dispersive waves with a generic resonant structure (roughly speaking, space and time resonant sets intersect transversally). We derive an asymptotic equivalent of the solution for data in the Schwartz class, and bilinear dispersive estimates for data in weighted Lebesgue spaces. An application to water waves with infinite depth, gravity and surface tension is also presented.

Original languageEnglish (US)
Pages (from-to)617-669
Number of pages53
JournalArchive for Rational Mechanics and Analysis
Volume214
Issue number2
DOIs
StatePublished - Sep 1 2014

Fingerprint

Bilinear Estimates
Dispersive Estimates
Water waves
Surface tension
Three-dimension
Two Dimensions
Gravitation
Weighted Lebesgue Spaces
Water Waves
Intersect
Surface Tension
Gravity
Interaction
Class

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

Bilinear Dispersive Estimates Via Space Time Resonances, Dimensions Two and Three. / Bernicot, Frédéric; Germain, Pierre.

In: Archive for Rational Mechanics and Analysis, Vol. 214, No. 2, 01.09.2014, p. 617-669.

Research output: Contribution to journalArticle

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