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arXiv · 2407.18508

On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations

Gigliola Staffilani·Minh-Binh Tran
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Abstract

Inspired by the fundamental work of Escobedo and Velazquez \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}, we prove that solutions of 4-wave kinetic equations, under very general forms of the dispersion relations, exhibit the transfer of energy towards large values of wavenumbers as time evolves. We also provide a global well-posedness theory for mild solutions of the equation under general forms of the dispersion relations.

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Gigliola Staffilani, Minh-Binh Tran. 2024-07-26. On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations. https://arxiv.org/abs/2407.18508

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