$ L^2 $-四波动力学方程的近平衡稳定性

IF 1 4区数学 Q1 MATHEMATICS Kinetic and Related Models Pub Date : 2022-10-20 DOI:10.3934/krm.2023031

A. Menegaki

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引用次数: 1

摘要

考虑了波浪湍流理论中出现的四波空间齐次动力学方程。我们研究了围绕瑞利-金斯平衡解的长期行为和解的存在性。对于截止频率，我们证明了在二次型情况下弱摄动的色散关系，在Rayleigh-Jeans平衡附近的线性化算子是强制的。然后我们传递到完全非线性算子，显示了接近瑞利-金斯的初始数据的$L^2$ -稳定性。

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$ L^2 $-stability near equilibrium for the 4 waves kinetic equation

We consider the four waves spatial homogeneous kinetic equation arising in wave turbulence theory. We study the long-time behaviour and existence of solutions around the Rayleigh-Jeans equilibrium solutions. For cut-off'd frequencies, we show that for dispersion relations weakly perturbed around the quadratic case, the linearized operator around the Rayleigh-Jeans equilibria is coercive. We then pass to the fully nonlinear operator, showing an $L^2$ - stability for initial data close to Rayleigh-Jeans.

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.