CNA Working Group Seminar
Jian-Guo Liu
Duke University
Title: Global existence and vortex blob methods for Camassa-Holm equations

Abstract: This talk is about the well-posedness of the Camassa-Holm equation and the modified Camassa-Holm equation. Local in time classical solutions, finite time blow-up behavior, life-span of classical solutions and global weak solutions are considered. Before blow-up time, we use Lagrange dynamics to analyze the classical solutions. After blow-up time, we use vortex blob methods to obtain global weak solutions.

References

[1] A. Chertock, J.-G. Liu, and T. Pendleton, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, SIAM J. Numer. Anal., 50 (2012) 1-21.

[2] Y. Duan and J.-G. Liu. Convergence analysis of the vortex blob method for the b-equation. Discrete Contin. Dyn. Syst. Ser. A, 34(2014) 1995-2011.

[3] G. Gui, Y. Liu, P. Oliver and C. Qu. Wave-breaking and peakons for a modified Camassa-Holm equation. Comm. Math. Phys. 319(2013) 731-759.

[4] Y. Gao and J.-G. Liu. Global convergence of particle method for modified Camassa-Holm equation. Preprint.

[5] Y. Gao and J.-G. Liu. Modified Camassa-Holm equation in Lagrage coordinate. Preprint.

Date: Tuesday, October 18, 2016
Time: 2:30 pm
Location: Wean Hall 7218
Submitted by:  Gautam Iyer