Local Well-posedness for the Kinetic MMT Model

Local Well-posedness for the Kinetic MMT Model

The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is believed to give a way to predict turbulent spectra. We clarify the formulation of the problem, and we develop the local...

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Veröffentlicht in:Communications in mathematical physics 2025, Vol.406 (1)
Hauptverfasser: Germain, Pierre, La, Joonhyun, Zhang, Katherine Zhiyuan
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Hamiltonian functions
Kinetic equations
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Turbulence
Well posed problems
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Zusammenfassung:The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system, which is believed to give a way to predict turbulent spectra. We clarify the formulation of the problem, and we develop the local well-posedness theory for this equation. Our analysis uncovers a surprising nonlinear smoothing phenomenon.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-05205-1