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

Gezi Chong; Jianxia He; Gezi Chong; Jianxia He

doi:10.3934/era.2025022

Electronic Research Archive

2025, Volume 33, Issue 1: 447-470. doi: 10.3934/era.2025022

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Research article

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

Gezi Chong ^{1
,
,},
Jianxia He ²

1.
School of Mathematics, Northwest University, Xi'an 710127, China
2.
School of Mathematics, Xi'an University of Finance and Economics, Xi'an 710100, China

Received: 15 October 2024 Revised: 23 December 2024 Accepted: 20 January 2025 Published: 24 January 2025

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.
- (3 + 1)-dimensional modified Zakharov-Kuznetsov equation,
- exponential decay,
- energy estimate
Citation: Gezi Chong, Jianxia He. On exponential decay properties of solutions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation[J]. Electronic Research Archive, 2025, 33(1): 447-470. doi: 10.3934/era.2025022

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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.

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