On the kinetic equation in zakharov's wave turbulence theory for capillary waves

Toan T. Nguyen; Minh Binh Tran

doi:10.1137/17M1125042

On the kinetic equation in zakharov's wave turbulence theory for capillary waves

Toan T. Nguyen
, Minh Binh Tran

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

18 Scopus citations

Abstract

The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived by physicists in the 1960s, though the well-posedness theory remains open due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution-the first such result-to the wave turbulence equation for capillary waves.

Original language	English (US)
Pages (from-to)	2020-2047
Number of pages	28
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	2
DOIs	https://doi.org/10.1137/17M1125042
State	Published - 2018

All Science Journal Classification (ASJC) codes

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/17M1125042

Cite this

@article{75eec5a0bd4f44eaafa0ed3cedba9bd6,

title = "On the kinetic equation in zakharov's wave turbulence theory for capillary waves",

abstract = "The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived by physicists in the 1960s, though the well-posedness theory remains open due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution-the first such result-to the wave turbulence equation for capillary waves.",

author = "Nguyen, \{Toan T.\} and Tran, \{Minh Binh\}",

note = "Funding Information: ∗Received by the editors April 10, 2017; accepted for publication (in revised form) January 22, 2018; published electronically April 10, 2018. http://www.siam.org/journals/sima/50-2/M112504.html Funding: The research of the first author was partially supported by NSF grant DMS-1405728. The research of the second author was supported by NSF grant RNMS (Ki-Net) 1107291 and ERC Advanced grant DYCON. †Department of Mathematics, Pennsylvania State University, State College, PA 16802 (nguyen@ math.psu.edu). ‡Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (mtran23@ wisc.edu). Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",

year = "2018",

doi = "10.1137/17M1125042",

language = "English (US)",

volume = "50",

pages = "2020--2047",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - On the kinetic equation in zakharov's wave turbulence theory for capillary waves

AU - Nguyen, Toan T.

AU - Tran, Minh Binh

N1 - Funding Information: ∗Received by the editors April 10, 2017; accepted for publication (in revised form) January 22, 2018; published electronically April 10, 2018. http://www.siam.org/journals/sima/50-2/M112504.html Funding: The research of the first author was partially supported by NSF grant DMS-1405728. The research of the second author was supported by NSF grant RNMS (Ki-Net) 1107291 and ERC Advanced grant DYCON. †Department of Mathematics, Pennsylvania State University, State College, PA 16802 (nguyen@ math.psu.edu). ‡Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (mtran23@ wisc.edu). Publisher Copyright: © 2018 Society for Industrial and Applied Mathematics.

PY - 2018

Y1 - 2018

N2 - The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived by physicists in the 1960s, though the well-posedness theory remains open due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution-the first such result-to the wave turbulence equation for capillary waves.

AB - The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived by physicists in the 1960s, though the well-posedness theory remains open due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution-the first such result-to the wave turbulence equation for capillary waves.

UR - https://www.scopus.com/pages/publications/85046865620

UR - https://www.scopus.com/pages/publications/85046865620#tab=citedBy

U2 - 10.1137/17M1125042

DO - 10.1137/17M1125042

M3 - Article

AN - SCOPUS:85046865620

SN - 0036-1410

VL - 50

SP - 2020

EP - 2047

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

On the kinetic equation in zakharov's wave turbulence theory for capillary waves

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this