On decay and regularity of solutions to the modified 2D Zakharov-Kuznetsov equation

TL;DR

This paper investigates how the regularity of solutions to the 2D modified Zakharov-Kuznetsov equation influences their decay properties in weighted Sobolev spaces, establishing key relations between these aspects.

Contribution

It provides new insights into the interplay between regularity and decay for solutions of the 2D modified Zakharov-Kuznetsov equation in weighted Sobolev spaces.

Findings

Established the relation between regularity and decay of solutions.

Characterized decay rates in weighted Sobolev spaces.

Provided conditions for decay based on regularity levels.

Abstract

This work is devoted to study the relation between regularity and decay for solutions of the two-dimensional modified Zakharov-Kuznetsov equation in the weighted Sobolev spaces $Z_{s,(r_1,r_2)}:=H^s(\R^2)\cap L^2((1+|x|^{2r_1}+|y|^{2r_2})dxdy)$.