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

2020/08/25 by Argenis J. Méndez, Mendez, A. J. · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2008.11252

openalex publication_date 2020/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 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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