On the onset of correlations in Wave Turbulence close to singularities

M. Escobedo; J. J. L. Velázquez

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arXiv · 2605.02540

On the onset of correlations in Wave Turbulence close to singularities

M. Escobedo·J. J. L. Velázquez

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Abstract

In this paper we describe in a formal way how the derivation of the turbulent wave equation for the Schr\"odinger equation breaks down for times close to the self similar blow up of the wave turbulence kinetic equation. To this end, we study how the derivation of the cumulants hierarchy can not be approximated using solutions of the wave turbulence kinetic equation near the blow up time. It tuns out that near the blow up time the kinetic equation has to be replaced by a hierarchy of equations which is equivalent to a random field, defined for times $t\in (-\infty, \infty)$ and satisfying a nonlinear non autonomous Schr\"odinger equation.

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M. Escobedo, J. J. L. Velázquez. 2026-05-04. On the onset of correlations in Wave Turbulence close to singularities. https://arxiv.org/abs/2605.02540

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