Well-posedness results for the 3D Zakharov-Kuznetsov equation

Francis Ribaud; Stéphane Vento

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arXiv · 1111.2850

Well-posedness results for the 3D Zakharov-Kuznetsov equation

Francis Ribaud·Stéphane Vento

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Abstract

We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\partial_tu+\Delta\partial_xu+ u\partial_xu=0$ in the Sobolev spaces $H^s(\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\R^3)$. The proof is based on a sharp maximal function estimate in time-weighted spaces.

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Francis Ribaud, Stéphane Vento. 2011-11-11. Well-posedness results for the 3D Zakharov-Kuznetsov equation. https://arxiv.org/abs/1111.2850

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