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

Toan T. Nguyen, Minh Binh Tran

Research output: Contribution to journalArticle

7 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 languageEnglish (US)
Pages (from-to)2020-2047
Number of pages28
JournalSIAM Journal on Mathematical Analysis
Volume50
Issue number2
DOIs
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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