Abstract
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 example, but also around a periodic solution, that is, to consider localized non-periodic perturbations of periodic solutions. Additionally, we show the global well-posedness in the energy space $H^1(\mathbb R ^2)$.
Citation
José Manuel Palacios. "Local well-posedness for the Zakharov-Kuznetsov equation on the background of a bounded function." Adv. Differential Equations 29 (9/10) 655 - 726, September/October 2024. https://doi.org/10.57262/ade029-0910-655
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