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

Frédéric Bernicot; Pierre Germain

doi:10.1007/s00205-014-0764-7

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

Frédéric Bernicot, Pierre Germain

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	617-669
Number of pages	53
Journal	Archive for Rational Mechanics and Analysis
Volume	214
Issue number	2
DOIs	https://doi.org/10.1007/s00205-014-0764-7
State	Published - Sep 1 2014

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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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.",

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AB - 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.

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

Abstract

ASJC Scopus subject areas

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