Math @ Duke

Publications [#335608] of JianGuo Liu
Papers Published
 Gao, Y; Li, L; Liu, JG, A dispersive regularization for the modified camassa–holm equation,
Siam Journal on Mathematical Analysis, vol. 50 no. 3
(January, 2018),
pp. 28072838, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/05/20)
Abstract: © 2018 Society for Industrial and Applied Mathematics In this paper, we present a dispersive regularization approach to construct a global Npeakon weak solution to the modified Camassa–Holm equation (mCH) in one dimension. In particular, we perform a double mollification for the system of ODEs describing trajectories of Npeakon solutions and obtain N smoothed peakons without collisions. Though the smoothed peakons do not give a solution to the mCH equation, the weak consistency allows us to take the smoothing parameter to zero and the limiting function is a global Npeakon weak solution. The trajectories of the peakons in the constructed solution are globally Lipschitz continuous and do not cross each other. When N = 2, the solution is a sticky peakon weak solution. At last, using the Npeakon solutions and through a mean field limit process, we obtain global weak solutions for general initial data m0 in Radon measure space.


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