On the Cauchy problem for a two-component Degasperis-Procesi system

TL;DR

This paper investigates the well-posedness and blow-up behavior of solutions to a two-component Degasperis-Procesi system, providing new criteria and rates for solution blow-up in specific function spaces.

Contribution

It establishes local well-posedness in Besov spaces, derives blow-up scenarios, and introduces new blow-up criteria and exact blow-up rates for the system.

Findings

Established local well-posedness in nonhomogeneous Besov spaces.

Derived precise blow-up scenarios for strong solutions.

Presented new blow-up criteria and exact blow-up rates.

Abstract

This paper is concerned with the Cauchy problem for a two-component Degasperis-Procesi system. Firstly, the local well-posedness for this system in the nonhomogeneous Besov spaces is established. Then the precise blow-up scenario for strong solutions to the system is derived. Finally, two new blow-up criterions and the exact blow-up rate of strong solutions to the system are presented.