On the Cauchy problem for a periodic rotation-two-component μ-Hunter–Saxton system

ABSTRACT

A new rotation-two-component $\mu$-Hunter–Saxton system is considered in the spatially periodic setting. The local well-posedness for the system is established by Kato theory. Two wave-breaking criteria and the sufficient conditions of blow-up solution are derived by relying on the Riccati differential equation and localization analysis. In addition, the Lyapunov function method is used to prove the existence of global solutions under certain conditions.

KEYWORDS:

• Rotation-two-component $\mu$-Hunter–Saxton system
• local well-posedness
• wave-breaking
• global existence

AMS SUBJECT CLASSIFICATIONS:

• 35D05
• 35G25
• 35L05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Guo’s work is supported by Zunyi Normal University doctoral program fund [grant number BS[2017]10], Department of Sichuan Province Education Fund [grand number 17ZB0314], Department of Sci-Tech of Guizhou Fund [grant number qian Ke He Ji Chu [2017]1201] and Natural Science Foundation of china NSFC [grant number 11661084]. Lai’s work is supported by Natural Science Foundation of china NSFC [grant number 11471263].