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arXiv · 2008.06946

Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data

Hong Cai·Geng Chen·Hongwei Mei
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Abstract

We give a proof for the uniqueness of dissipative solution for the Camassa-Holm equation with some peakon-antipeakon initial data following Dafermos' earlier resut in [5] on the Hunter-Saxton equation. Our result shows that two existing global existence frameworks, through the vanishing viscosity method by Xin-Zhang in [11] and the transformation of coordinate method for dissipative solutions by Bressan-Constantin in [3], give the same solution, for a special but typical initial data forming finite time gradient blowup.

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Hong Cai, Geng Chen, Hongwei Mei. 2020-08-16. Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data. https://arxiv.org/abs/2008.06946

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