Almost sharp wave kinetic theory of multidimensional KdV type equations with d≥ 3

2022/04/13 by Xiao Ma, Ma, Xiao
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2204.06148

openalex publication_date 2022/04/13 · openalex created_date 2022/04/26 · openalex updated_date 2026/07/28

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^-εT_kin. Our result reaches kinetic time scale up to ε loss.

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