2017/07/20 by Yu Gao, Lei Li, Gao, Yu +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1707.06377
openalex publication_date 2017/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a dispersive regularization for the modified Camassa-Holm equation (mCH) in one dimension, which is achieved through a double mollification for the system of ODEs describing trajectories of N-peakon solutions. From this regularized system of ODEs, we obtain approximated N-peakon solutions with no collision between peakons. Then, a global N-peakon solution for the mCH equation is obtained, whose trajectories are global Lipschitz functions and do not cross each other. When N=2, the limiting solution is a sticky peakon weak solution. By a limiting process, we also derive a system of ODEs to describe N-peakon solutions. At last, using the N-peakon solutions and through a mean field limit process, we obtain global weak solutions for general initial data m0 in Radon measure space.