Stability of Rayleigh-Jeans equilibria in the kinetic FPU equation

2024/09/03 by Germain, Pierre, La, Joonhyun, Menegaki, Angeliki · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2409.01507

Abstract

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.

Cited by

• Long-Time Existence and Behavior of Solutions to the Inhomogeneous Kinetic FPU Equation
• 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

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