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

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

2011-11-11

arxiv.org/abs/1111.2850v1

Mathematics

Analysis of PDEs

Scientific paper

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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