Pierre Germain, Joonhyun La, Katherine Zhiyuan Zhang
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Abstract
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.
期刊介绍：
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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