Optimal local well-posedness theory for the kinetic wave equation

Pierre Germain, Alexandru D. Ionescu, Minh Binh Tran

Research output: Contribution to journalArticle

Abstract

We prove local existence and uniqueness results for the (space-homogeneous) 4-wave kinetic equation in wave turbulence theory. We consider collision operators defined by radial, but general dispersion relations satisfying suitable bounds, and we prove two local well-posedness theorems in nearly critical weighted spaces.

Original languageEnglish (US)
Article number108570
JournalJournal of Functional Analysis
DOIs
StateAccepted/In press - Jan 1 2020

Keywords

  • Nonlinear Schrödinger
  • Quantum Boltzmann
  • Wave (weak) turbulence
  • Wave kinetic equations

ASJC Scopus subject areas

  • Analysis

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