Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 11, pp. 1-41.

Title: Smoothing properties for a coupled Zakharov-Kuznetsov system
       
Authors: Julie L. Levandosky (Framingham State Univ., Framingham, MA USA)
         Octavio Vera (Univ. de Tarapaca, Arica, Chile)
         
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 (u<sub>0</sub>,v<sub>0</sub>) possesses certain
regularity and sufficient decay as x &rarr; &infin;, then the solution
(u(t),v(t)) will be smoother than (u<sub>0</sub>, v<sub>0</sub>)
for 0 &lt; t &le; T where T is the existence time of the solution.

Submitted April 18, 2022. Published February 4, 2023.
Math Subject Classifications: 35Q53, 35Q35, 47J35.
Key Words: Coupled Zakharov-Kuznetsov system; gain in regularity; weighted Sobolev space.