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Research Article | Open Access

On exponential decay properties of solutions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation

Gezi Chong1( ), Jianxia He2
School of Mathematics, Northwest University, Xi'an 710127, China
School of Mathematics, Xi'an University of Finance and Economics, Xi'an 710100, China
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Abstract

We study here the special decay properties of real solutions to the initial value problem associated with the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation. More precisely, we prove the properties of exponential decay of order 3 / 2 above the plane x + y + z = 0 as time evolves. This property is related with the persistence properties of the solution flow in weighted Sobolev spaces and sharp unique continuation properties of solutions to this problem.

Keywords

(3 + 1)-dimensional modified Zakharov-Kuznetsov equationexponential decayenergy estimate

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Electronic Research Archive
Volume 33 Issue 1,
January 2025
Pages 447-470
DOI: 10.3934/era.2025022

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Cite this article:
Chong G, He J. On exponential decay properties of solutions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation. Electronic Research Archive, 2025, 33(1): 447-470. https://doi.org/10.3934/era.2025022

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Received: 15 October 2024
Revised: 23 December 2024
Accepted: 20 January 2025
Published: 15 January 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)