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arXiv · 1809.02027

On the periodic Zakharov-Kuznetsov equation

Felipe Linares·Mahendra Panthee·Tristan Robert·Nikolay Tzvetkov
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Abstract

We consider the Cauchy problem associated with the Zakharov-Kuznetsov equation, posed on $\mathbb{T}^2$. We prove the local well-posedness for given data in $H^s(\mathbb{T}^2)$ whenever $s>5/3$. More importantly, we prove that this equation is of quasi-linear type for initial data in any Sobolev space on the torus, in sharp contrast with its semi-linear character in the $\mathbb{R}^2$ and $\mathbb{R}\times \mathbb{T}$ settings.

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Felipe Linares, Mahendra Panthee, Tristan Robert, Nikolay Tzvetkov. 2018-09-06. On the periodic Zakharov-Kuznetsov equation. https://arxiv.org/abs/1809.02027

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