Uniqueness of conservative solutions to the the modified Camassa-Holm equation via Characteristics

Zhen He; Zhaoyang Yin

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arXiv · 2310.15726

Uniqueness of conservative solutions to the the modified Camassa-Holm equation via Characteristics

Zhen He·Zhaoyang Yin

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Abstract

In this paper,for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get the uniqueness of the conservative solution in the original variables.

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Zhen He, Zhaoyang Yin. 2023-10-24. Uniqueness of conservative solutions to the the modified Camassa-Holm equation via Characteristics. https://arxiv.org/abs/2310.15726

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