Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher

Abstract

The Zakharov-Kuznetsov equation in space dimension $d\ge 3$ is considered. It is proved that the Cauchy problem is locally well-posed in $H^s({\mathbb{R}}^d)$ in the full subcritical range $s>(d-4)/2$, which is optimal up to the endpoint. As a corollary, global well-posedness in $L^2({\mathbb{R}}^3)$ and, under a smallness condition, in $H^1({\mathbb{R}}^4)$, follow.

Almost orthogonal decompositions from arXiv:1905.01490 [math.AP] are adapted to the higher dimensional setting

References in corpus (2)

• Convolutions of singular measures and applications to the Zakharov system
• On the 2d Zakharov system with L^2 Schrödinger data

Cited by in corpus (3)

• Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation
• Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
• Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation