Instability of singular equilibria of a wave kinetic equation

Autor:	Escobedo, Miguel, Menegaki, Angeliki
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	We consider the singular Rayleigh-Jeans equilibrium of the $4$-waves kinetic turbulence equation for the three dimensional Schr\"{o}dinger equation. We first show the formation in finite time of a Dirac measure at zero frequency in the solution of the wave kinetic equation when the initial data has the form of Rayleigh-Jeans, truncated at large values of the energy. The initial value problem for the linearization around the singular Rayleigh-Jeans equilibria is then solved in several functional spaces. Then, long time convergence to a Dirac measure at the origin is described in detail for some of the solutions. This determines a basin of attraction of the Dirac measure. Comment: 43 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.05280 Zobrazit plný text záznamu View this record from Arxiv