Optimal local well-posedness theory for the kinetic wave equation

Pierre Germain; Alexandru D. Ionescu; Minh Binh Tran

doi:10.1016/j.jfa.2020.108570

Optimal local well-posedness theory for the kinetic wave equation

Pierre Germain, Alexandru D. Ionescu, Minh Binh Tran

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

13 Scopus citations

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 language	English (US)
Article number	108570
Journal	Journal of Functional Analysis
Volume	279
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2020.108570
State	Published - Sep 1 2020
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

Keywords

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

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10.1016/j.jfa.2020.108570

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title = "Optimal local well-posedness theory for the kinetic wave equation",

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.",

keywords = "Nonlinear Schr{\"o}dinger, Quantum Boltzmann, Wave (weak) turbulence, Wave kinetic equations",

author = "Pierre Germain and Ionescu, {Alexandru D.} and Tran, {Minh Binh}",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

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doi = "10.1016/j.jfa.2020.108570",

language = "English (US)",

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T1 - Optimal local well-posedness theory for the kinetic wave equation

AU - Germain, Pierre

AU - Ionescu, Alexandru D.

AU - Tran, Minh Binh

PY - 2020/9/1

Y1 - 2020/9/1

N2 - 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.

AB - 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.

KW - Nonlinear Schrödinger

KW - Quantum Boltzmann

KW - Wave (weak) turbulence

KW - Wave kinetic equations

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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Optimal local well-posedness theory for the kinetic wave equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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