Analysis of the kinetic equation arising from the one-dimensional FPUT chain
[Analyse de l’équation cinétique associée à la chaîne FPUT en dimension un]
Angeliki Menegaki1
1Department of Mathematics, Huxley building, South Kensington campus, Imperial College London, London SW7 2AZ, United Kingdom
Journées équations aux dérivées partielles (2025), Exposé no. 5, 9 p.

We briefly review the main results from Germain–La–Menegaki (2024) and Escobedo–Germain–La–Menegaki (2025) which (i) proves nonlinear stability of the non-singular Rayleigh–Jeans equilibria for the kinetic wave equation associated with the $\beta $-FPUT chain and (ii) classifies the entropy maximizers for a more general class of kinetic equations arising from such discrete systems. We briefly explain the main ideas and strategies for the proofs.

Nous présentons brièvement les principaux résultats de Germain–La–Menegaki (2024) et Escobedo–Germain–La–Menegaki (2025), qui (i) établissent la stabilité non linéaire des équilibres de Rayleigh–Jeans non singuliers pour l’équation cinétique associée à la chaîne $\beta $-FPUT, et (ii) classent les maximiseurs d’entropie pour une classe plus générale d’équations cinétiques issues de tels systèmes discrets. Nous esquissons également les idées et stratégies principales des démonstrations.

Publié le :
DOI : 10.5802/jedp.696
Classification : 82C70, 35B40, 76F55, 74A25, 82C40, 35Q20, 82C10
Keywords: weak wave turbulence, kinetic equations, Fermi–Pasta–Ulam–Tsingou chains, Rayleigh–Jeans equilibria, thermalisation, entropy maximisers, nonlinear stability
Mots-clés : turbulence faible des ondes, équations cinétiques, chaînes de Fermi–Pasta–Ulam–Tsingou, équilibres de Rayleigh–Jeans, thermalisation, maximiseurs d’entropie, stabilité non linéaire

Angeliki Menegaki  1

1 Department of Mathematics, Huxley building, South Kensington campus, Imperial College London, London SW7 2AZ, United Kingdom 
Angeliki Menegaki. Analysis of the kinetic equation arising from the one-dimensional FPUT chain. Journées équations aux dérivées partielles (2025), Exposé no. 5, 9 p.. doi: 10.5802/jedp.696
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