Abstract
In this paper, we are concerned with \begin{document}$N$\end{document} -Component Camassa-Holm equation with peakons. Firstly, we establish the local well-posedness in a range of the Besov spaces by using Littlewood-Paley decomposition and transport equation theory. Secondly, we present a precise blowup scenario and several blowup results for strong solutions to that system, we then obtain the blowup rate of strong solutions when a blowup occurs. Next, we investigate the persistence property for the strong solutions. Finally, we consider the initial boundary value problem, our approach is based on sharp extension results for functions on the half-line and several symmetry preserving properties of the equations under discussion.
Highlights
In this paper, we consider the following N -Component Camassa-Holm equation with peakons m1,t + m1,xu1 + 2m1u1,x + m1 m2,t + m2,xu2 + 2m2u2,x + m2 n j=1 uj +x n j=2 uj x n j=1 mj uj,x =0, n j=2 mj uj,x (1)mn,t + mn,xun + 2mnun,x + mn n j=n uj x n j=n mj uj,x0, where mi = ui − ui,xx, i = 1, 2, · · ·, n
In [37], the authors establish the local well-posedness of the initial value problem for system (1) with n = 3 and present a precise blowup scenario and several blowup results for strong solutions to that system
We present a precise blowup scenario, several blowup results for strong solutions to that system, we obtain the blowup rate of strong solutions to the system when a blowup occurs
Summary
We consider the following N -Component Camassa-Holm equation with peakons. In [37], the authors establish the local well-posedness of the initial value problem for system (1) with n = 3 and present a precise blowup scenario and several blowup results for strong solutions to that system. They determine the blowup rate of strong solutions to the system when a blowup occurs. We shall establish local well-posedness of the initial value problem (1) in the Besov spaces
Sign-in/Register to view highlights & summary 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.
