Global existence and blow-up phenomena for a periodic 2-component Camassa-Holm equation with vorticity
Qiaoyi Hu, Zhaoyang Yin
TL;DR
This paper investigates the mathematical behavior of a periodic 2-component Camassa-Holm equation with vorticity, establishing conditions for global solutions and blow-up phenomena, and analyzing their rates.
Contribution
It provides the first local well-posedness, global existence, and blow-up results for this specific vorticity-inclusive Camassa-Holm model.
Findings
Established local well-posedness of solutions.
Proved global existence for strong solutions.
Derived blow-up conditions and rates.
Abstract
We first establish local well-posedness for a periodic 2-component Camassa-Holm equation with vorticity. We then present a global existence result for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Differential Equations and Dynamical Systems