On the modified multi-component Camassa-Holm system in higher dimensions

TL;DR

This paper investigates the modified multi-component Camassa-Holm system in higher dimensions, establishing local well-posedness in Besov spaces and deriving blow-up criteria for strong solutions.

Contribution

It provides the first almost complete local well-posedness results and blow-up criteria for this higher-dimensional system.

Findings

Established local well-posedness in Besov spaces

Derived blow-up criteria using Littlewood-Paley decomposition

Analyzed energy methods for solution behavior

Abstract

This paper is devoted to the Cauchy problem for the modified multi-component Camassa-Holm system in higher dimensions. On the one hand, we establish an almost complete local well-posedness results for the system in the framework of Besov spaces. On the other hand, several blow-up criteria of strong solutions to the system are derived by using the Littlewood-Paley decomposition and the energy method.