Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function
Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function
We prove the local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in $H^s(\mathbb R ^2)$, for $s\in [1,2]$, on the background of an $L^\infty(\mathbb R ^3)$-function $\Psi(t,x,y)$, with $\Psi(t,x,y)$ satisfying some natural extra conditions. This result not only gives us a framework to solve the ZK equation around a Kink, for …