Local Well-posedness for the Kinetic MMT Model

IF 2.2 1区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Mathematical Physics Pub Date : 2024-12-18 DOI:10.1007/s00220-024-05205-1
Pierre Germain, Joonhyun La, Katherine Zhiyuan Zhang
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引用次数: 0

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.

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动力学 MMT 模型的局部均衡性
MMT 方程由 Majda、McLaughlin 和 Tabak 提出,作为研究波湍流的模型。我们重点研究了与该哈密顿系统相关的动力学方程,该方程被认为是预测湍流频谱的一种方法。我们澄清了问题的表述,并发展了该方程的局部好拟性理论。我们的分析发现了一个令人惊讶的非线性平滑现象。
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来源期刊
Communications in Mathematical Physics
Communications in Mathematical Physics 物理-物理:数学物理
CiteScore
4.70
自引率
8.30%
发文量
226
审稿时长
3-6 weeks
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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