Local classical solutions of a kinetic equation for three waves interactions in presence of a Dirac measure at the origin

Miguel Escobedo

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arXiv · 2505.00267

Local classical solutions of a kinetic equation for three waves interactions in presence of a Dirac measure at the origin

Miguel Escobedo

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Abstract

The existence of local, classical solutions is proved, for a system of two coupled equations that describe, in the framework of the wave turbulence theory, the fluctuations around an equilibrium, of a system of nonlinear waves satisfying the 3-d cubic Schr\"odinger equation, weakly interacting in presence of a condensate. The function that describes the density of waves behaves like a singular Rayleigh Jeans equilibria near the origin, and induces a strictly increasing behavior in time of the function describing the condensate's density.

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Miguel Escobedo. 2025-05-01. Local classical solutions of a kinetic equation for three waves interactions in presence of a Dirac measure at the origin. https://arxiv.org/abs/2505.00267

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