Local Well-posedness for the Kinetic MMT Model

Joonhyun La; Katherine Zhiyuan Zhang; Pierre Germain

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

Local Well-posedness for the Kinetic MMT Model

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

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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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