Subcritical wellposedness results for the ZakharovKuznetsov equation in dimension three and higher
Abstract
The ZakharovKuznetsov equation in space dimension $d\geq 3$ is considered. It is proved that the Cauchy problem is locally wellposed in $H^s(\mathbb{R}^d)$ in the full subcritical range $s>(d4)/2$, which is optimal up to the endpoint. As a corollary, global wellposedness in $L^2(\mathbb{R}^3)$ and, under a smallness condition, in $H^1(\mathbb{R}^4)$, follow.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.09047
 Bibcode:
 2020arXiv200109047H
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 Almost orthogonal decompositions from arXiv:1905.01490 [math.AP] are adapted to the higher dimensional setting