Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schr{ö}dinger equation with well prepared random initial data
Year: 2026
Type: preprint
Abstract: We prove a long time well-posedness result for a quadratic non-linear Schr{ö}dinger equation with random well prepared initial conditions in dimension d $\ge$ 1. In some regimes, we derive the Wave Kinetic equation associated with the equation in dimension d $\ge$ 5, almost up to the kinetic time to the power d/(d + 1). Our analysis relies on the ideas introduced by Deng and Hani.
Source: arXiv (Cornell University)
Author: Brun, Enguerrand
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214182234