Year: 2024
Type: preprint
Abstract: We describe regularizing effects in the linearization of a kinetic equation that arises in study of a system of nonlinear waves satisfying the Schrödinger equation in terms of weak turbulence and condensate. The problem is first considered in spaces of bounded functions with weights, where existence of solutions and some first regularity properties are proved. After a suitable change of variables the equation is written in terms of a pseudo differential operator. Homogeneity of the equation and classical arguments of freezing of coefficients may then be used to prove regularizing effect in local Sobolev type spaces.
Source: arXiv (Cornell University)
Author: Escobedo, Miguel
Institution: University of the Basque Country
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390810552