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arXiv · 1702.02610

On the unique continuation property of solutions of the three-dimensional Zakharov-Kuznetsov equation

Eddye Bustamante·José Jiménez Urrea·Jorge Mejía
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Abstract

We prove that if the difference of two sufficiently smooth solutions of the three-dimensional Zakharov-Kuznetsov equation $$\partial_{t}u+\partial_{x}\triangle u+u\partial_{x}u=0 \text{,}\quad (x,y,z)\in\mathbb R^3, \;t\in[0,1],$$ decays as $e^{-a(x^2+y^2+z^2)^{3/4}}$ at two different times, for some $a>0$ large enough, then both solutions coincide.

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Eddye Bustamante, José Jiménez Urrea, Jorge Mejía. 2017-02-08. On the unique continuation property of solutions of the three-dimensional Zakharov-Kuznetsov equation. https://arxiv.org/abs/1702.02610

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