Affiliation:
1. Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile
Abstract
In this paper, we focus on the Zakharov–Kuznetsov (ZK) equation in the [Formula: see text]-dimensional setting with [Formula: see text] and investigate its smoothness properties. We extend the well-known regularity propagation phenomenon observed in the 2D and 3D cases, where the regularity of the initial data on certain half-spaces propagates with infinite speed, to the case where the regularity of the initial data is measured on a fractional scale. To achieve this, we introduce new localization formulas that enable us to describe the regularity of the solution on a specific class of subsets in Euclidean space. This work provides insights into the regularity behavior of solutions of the ZK equation in higher dimensions and with more general initial data.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Analysis