The existence of strong solutions to the $3D$ Zakharov-Kuznestov equation in a bounded domain
The existence of strong solutions to the $3D$ Zakharov-Kuznestov equation in a bounded domain
We consider the Zakharov-Kuznestov (ZK) equation posed in a limited domain $\mathcal{M}=(0,1)_{x}\times(-\pi /2, \pi /2)^d,$ $ d=1,2$ supplemented with suitable boundary conditions. We prove that there exists a solution $u \in \mathcal C ([0, T]; H^1(\mathcal{M})) $ to the initial and boundary value problem for the ZK equation in both …