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arXiv · 2409.05550

Dispersive decay for the mass-critical generalized Korteweg-de Vries equation and generalized Zakharov-Kuznetsov equations

Minjie Shan
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Abstract

In this paper, we discuss pointwise decay estimate for the solution to the mass-critical generalized Korteweg-de Vries (gKdV) equation with initial data $u_0\in H^{1/2}(\mathbb{R})$. It is showed that nonlinear solution enjoys the same decay rate as linear one. Moreover, we also quantify the decay for solutions to the generalized Zakharov-Kuznetsov equation which is a natural multi-dimensional extension of the gKdV equation. We obtain some decay estimates for nonlinear solutions to generalized Zakharov-Kuznetsov equations with small initial data in $H^2(\mathbb{R}^d)$.

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Minjie Shan. 2024-09-09. Dispersive decay for the mass-critical generalized Korteweg-de Vries equation and generalized Zakharov-Kuznetsov equations. https://arxiv.org/abs/2409.05550

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