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Condensation and non-condensation times for 4-wave kinetic equations

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arxiv 2407.18533 v1 pith:P3TEYBPT submitted 2024-07-26 math-ph math.MP

Gigliola Staffilani , Minh-Binh Tran This is my paper · ORCID
classification math-phmath.MP
keywords escobedovelazquezcitecondensationequationskineticnon-condensationsolutionstimes
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Inspired by the pioneering 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 dispersion relations, develop condensation at the origin in finite time, under weaker conditions on the initial data than the ones considered in \cite{EscobedoVelazquez:2015:FTB,EscobedoVelazquez:2015:OTT}. We also provide some estimates on the non-condensation times of the solutions.

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  1. Entropy Structures and Long-Time Relaxation for 3-Wave Kinetic Equations

    math.AP 2026-05 unverdicted novelty 8.0 of 10

    New entropy structures from one-sided balance conditions on interaction weights yield global weak L1_loc solutions to 3-wave kinetic equations and prove their local relaxation to zero equilibrium.

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