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arXiv · 1401.0312

Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics

Alberto Bressan·Geng Chen·Qingtian Zhang
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Abstract

The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution $u=u(t,x)$, an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities $u$ and $v= 2\arctan u_x$ along each characteristic, it is proved that the Cauchy problem with general initial data $u_0\in H^1(\mathbb{R})$ has a unique solution, globally in time.

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Alberto Bressan, Geng Chen, Qingtian Zhang. 2014-01-01. Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics. https://arxiv.org/abs/1401.0312

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