On the propagation of regularity for solutions of the Zakharov-Kuznetsov equation

A. J. Mendez

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arXiv · 2008.11252

On the propagation of regularity for solutions of the Zakharov-Kuznetsov equation

A. J. Mendez

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Abstract

In this work, we study some special properties of smoothness concerning to the initial value problem associated with the Zakharov-Kuznetsov-(ZK) equation in the $n-$ dimensional setting, $n\geq 2.$ It is known that the solutions of the ZK equation in the $2d$ and $3d$ cases verify special regularity properties. More precisely, the regularity of the initial data on a family of half-spaces propagates with infinite speed. Our objective in this work is to extend this analysis to the case in that the regularity of the initial data is measured on a fractional scale. To describe this phenomenon we present new localization formulas that allow us to portray the regularity of the solution on a certain class of subsets of the euclidean space.

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A. J. Mendez. 2020-08-25. On the propagation of regularity for solutions of the Zakharov-Kuznetsov equation. https://arxiv.org/abs/2008.11252

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