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Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation

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arxiv 2409.01507 v1 pith:FJ7UEKJL submitted 2024-09-03 math.AP math-phmath.MP

Pierre Germain , Joonhyun La , Angeliki Menegaki This is my paper
classification math.APmath-phmath.MP
keywords stabilityequationequilibriakineticnonlinearproblemrayleigh-jeansable
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We study the nonlinear dynamics of the kinetic wave equation associated to the FPU problem and prove stability of the non-singular Rayleigh-Jeans equilibria. The lack of a spectral gap for the linearized problem leads to polynomial decay, which we are able to leverage to obtain nonlinear stability.

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  1. Sharp decay thresholds in weighted $L^\infty$ for wave kinetic equations with power-law dispersion

    math.AP 2026-07 conditional novelty 6.0 of 10

    Four-wave kinetic equations with dispersion |p|^a and kernel growth |p|^{2β} in 3D are locally well-posed in weighted L∞ exactly above the decay threshold s_c = 4β + 3 − a/2, with ill-posedness below.

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