Supercritical Zakharov-Kuznetsov equation posed on bounded rectangles (Q2026466)

The aim of this paper is to consider an initial boundary value problem for the 2D generalized Zakharov-Kuznetsov (gZK) equation : \[u_t+u_x+u^ku_x+u_{xxx}+u_{xyy}=0, \quad k\in\mathbb{N},\] posed on a bounded rectangle. The authors use the semigroup theory for the problem in abstract form and apply the fixed point method to find the local solution of gZK with \(k>2\). Supercritical (higher than two) integer powers in nonlinearity have been studied. Results on the existence, uniqueness and exponential decay of solutions are presented. The paper is organized as follows. Section 1, is an introduction to the subject. Section 2 deals with some preliminaries. Section 3 deals with local results and Section 4 with global estimates.