Global existence for capillary water waves

Pierre Germain; Nader Masmoudi; Jalal Shatah

doi:10.1002/cpa.21535

Global existence for capillary water waves

Pierre Germain, Nader Masmoudi, Jalal Shatah

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

Abstract

Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space-time resonance method and commuting vector fields.

Original language	English (US)
Pages (from-to)	625-687
Number of pages	63
Journal	Communications on Pure and Applied Mathematics
Volume	68
Issue number	4
DOIs	https://doi.org/10.1002/cpa.21535
State	Published - Apr 1 2015

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1002/cpa.21535

Cite this

@article{39b9fb8c9e8f413392abed69938998ed,

title = "Global existence for capillary water waves",

abstract = "Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space-time resonance method and commuting vector fields.",

author = "Pierre Germain and Nader Masmoudi and Jalal Shatah",

note = "Publisher Copyright: {\textcopyright} 2015 Wiley Periodicals, Inc.",

year = "2015",

month = apr,

day = "1",

doi = "10.1002/cpa.21535",

language = "English (US)",

volume = "68",

pages = "625--687",

journal = "Communications on Pure and Applied Mathematics",

issn = "0010-3640",

publisher = "Wiley-Liss Inc.",

number = "4",

}

TY - JOUR

T1 - Global existence for capillary water waves

AU - Germain, Pierre

AU - Masmoudi, Nader

AU - Shatah, Jalal

PY - 2015/4/1

Y1 - 2015/4/1

N2 - Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space-time resonance method and commuting vector fields.

AB - Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space-time resonance method and commuting vector fields.

UR - http://www.scopus.com/inward/record.url?scp=84923132209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923132209&partnerID=8YFLogxK

U2 - 10.1002/cpa.21535

DO - 10.1002/cpa.21535

M3 - Article

AN - SCOPUS:84923132209

SN - 0010-3640

VL - 68

SP - 625

EP - 687

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 4

ER -

Global existence for capillary water waves

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this