Abstract
We introduce and study an initial and boundary-value problem for the Zakharov-Kuznetsov equation posed on an infinite strip of ${\mathbb{R}^{d+1}}$, $d=1,2$. After establishing a suitable trace theorem, we first consider the linearized case and define the corresponding semigroup on $L^2$ and prove that it has a global smoothing effect. Then we proceed to the nonlinear case and use the smoothing effect to prove in both dimensions the existence of (unique when $d=1$) global weak solutions of the initial and boundary problem with null boundary conditions and $L^2$ initial data.
Citation
Jean-Claude Saut. Roger Temam. "An initial boundary-value problem for the Zakharov-Kuznetsov equation." Adv. Differential Equations 15 (11/12) 1001 - 1031, November/December 2010. https://doi.org/10.57262/ade/1355854433
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