Smoothing properties for a coupled Zakharov-Kuznetsov system

Abstract

In this article we study the smoothness properties of solutions to a two-dimensional coupled Zakharov-Kuznetsov system. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial data (u0,v0) possesses certain regularity and sufficient decay as x → ∞, then the solution (u(t),v(t)) will be smoother than (u0, v0) for 0 < t ≤ T where T is the existence time of the solution.