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Local Well-posedness for the Kinetic MMT Model

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arxiv 2310.11893 v1 pith:ZXMDTWMM submitted 2023-10-18 math.AP

Pierre Germain , Joonhyun La , Katherine Zhiyuan Zhang This is my paper · ORCID
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

    math.AP 2026-05 unverdicted novelty 8.0 of 10

    New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.

  2. On the ill-posedness of kinetic wave equations

    math.AP 2024-11 conditional novelty 7.0 of 10

    For kinetic wave equations from quasilinear Schrödinger models, local well-posedness in weighted L∞ spaces holds exactly when the derivative-loss parameter β ≤ 1/4, and fails for β > 1/4.

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