On the convergence rates of discrete solutions to the Wave Kinetic Equation

Autor:	Dolce, Michele, Grande, Ricardo
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics 35B40 45G05 35Q55
Druh dokumentu:	Working Paper
Popis:	In this paper, we consider the long-term behavior of some special solutions to the Wave Kinetic Equation (WKE). This equation provides a mesoscopic description of wave systems interacting nonlinearly via the cubic NLS equation. Escobedo and Vel\'azquez showed that, starting with initial data given by countably many Dirac masses, solutions remain a linear combination of countably many Dirac masses at all times. Moreover, there is convergence to a single Dirac mass at long times. The first goal of this paper is to give quantitative rates for the speed of said convergence. In order to study the optimality of the bounds we obtain, we introduce and analyze a toy model accounting only for the leading order quadratic interactions. Comment: 19 pages, comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.14400 Zobrazit plný text záznamu View this record from Arxiv