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arXiv · 2609.28093

Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schr{ö}dinger equation with well prepared random initial data

Enguerrand Brun
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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.

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Enguerrand Brun. 2026-09-23. Long time well-posedness and wave turbulence limit for a quadratic non-lienar Schr{ö}dinger equation with well prepared random initial data. https://arxiv.org/abs/2609.28093

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