Local Well-posedness for the Kinetic MMT Model

2023/10/18 by Pierre Germain, Germain, Pierre, Joonhyun La +3 · 2 citations
Mathematics · Engineering · #Gas Dynamics and Kinetic Theory #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2310.11893

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.

Cited by

• An energy cascade finite volume scheme for a mixed 3- and 4-wave kinetic equation arising from the theory of finite-temperature trapped Bose gases
• Numerical study of a nonlocal nonlinear Schrödinger equation (MMT model)

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