Almost sharp wave kinetic theory of multidimensional KdV type equations with $d\ge 3$

Xiao Ma

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arXiv · 2204.06148

Almost sharp wave kinetic theory of multidimensional KdV type equations with $d\ge 3$

Xiao Ma

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Abstract

In this work, we study the random series expansion of a multidimensional KdV type equation with a diffusion term, the so-called Zakharov-Kuznetsov (ZK) equation. We impose random initial data and periodic boundary condition with period $L$ on this equation. Using the random series expansion, we derive the $3$-wave kinetic equation on the inertial range for $t\lesssim L^{-\varepsilon}T_{\text{kin}}$. Our result reaches kinetic time scale up to $\varepsilon$ loss.

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Xiao Ma. 2022-04-13. Almost sharp wave kinetic theory of multidimensional KdV type equations with $d\ge 3$. https://arxiv.org/abs/2204.06148

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