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Almost sharp wave kinetic theory of multidimensional KdV type equations with $d\ge 3$
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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.
Forward citations
Cited by 3 Pith papers
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On the wave turbulence theory of 2D gravity waves, II: propagation of randomness
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For kinetic wave equations from quasilinear Schrödinger models, local well-posedness in weighted L∞ spaces holds exactly when the derivative-loss parameter β ≤ 1/4, and fails for β > 1/4.
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The $L^2$ contraction of solutions with large perturbation in multiple space dimensions from the oscillatory dispersive planar shock
Planar monotone and oscillatory dispersive shocks of dissipative KP and multi-D KdV–Burgers are L2-contractive under large multi-D perturbations up to Lipschitz shifts, under explicit viscosity–dispersion–strength bounds.
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