Abstract
The two-component μ-Hunter–Saxton system is considered in the spatially periodic setting. Firstly, two wave-breaking criteria are derived by employing the transport equation theory and the localization analysis method. Secondly, a sufficient condition of the blow-up solutions is established by using the classic method. The results obtained in this paper are new and different from those in previous works.
Highlights
1 Introduction In this article, we consider the periodic two-component μ-Hunter–Saxton system derived by Zuo [1]
The objective of the present paper is to focus mainly on wavebreaking criterion and several sufficient conditions of blow-up solutions
If t is replaced by –t, and γi = 0 (i = 1, 2) in system (1), system (1) has significant relationship with several models describing the motion of waves at the free surface of shallow water under the influence of gravity
Summary
We consider the periodic two-component μ-Hunter–Saxton system derived by Zuo [1]. If t is replaced by –t, and γi = 0 (i = 1, 2) in system (1), system (1) has significant relationship with several models describing the motion of waves at the free surface of shallow water under the influence of gravity Such as μ-Camassa–Holm equation [4,5,6], μ–b equation [7], two-component periodic Hunter–Saxton system [8,9,10,11,12], and twocomponent Dullin–Gottwald–Holm system [13, 14]. 3, we employ the transport equation theory to prove a wave-breaking criterion in the Sobolev space Hs(S) × Hs–1(S).
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