Abstract
The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.
Highlights
We will consider the periodic two-component μ-Hunter-Saxton system derived by Zuo [1]
Ρ (0, x) = ρ0 (x), x ∈ R, u (t, x + 1) = u (t, x), t > 0, x ∈ R, ρ (t, x + 1) = ρ (t, x), t > 0, x ∈ R, where u(t, x) and ρ(t, x) are time-dependent functions on the unit circle S = R/Z, μ(u) = ∫S u dx denotes its mean, and γi ∈ R, i = 1, 2. It is shown in [1] that system (1) is an Euler equation with bi-Hamilton structure
The objective of the present paper is to focus mainly on wavebreaking criterion and several sufficient conditions of blowup solutions
Summary
We will consider the periodic two-component μ-Hunter-Saxton system derived by Zuo [1]. Motivated by the works in [13, 20], in the present paper, the localization analysis in the transport equation theory is employed to derive a new wave-breaking criterion of solutions for the system (1) in the Sobolev space Hs(S) × Hs−1(S) with s ≥ 2. It implies that the wave-breaking criterion is determined only by the slope of the component u of solution definitely.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
