We give a proof for the uniqueness of dissipative solution for Camassa–Holm equation with some peakon–antipeakon initial data. Our result shows that two existing global existence frameworks, through the vanishing viscosity method by Xin–Zhang in Xin and Zhang (2000) and the transformation of coordinate method for dissipative solutions by Bressan–Constantin in Bressan and Constantin (2007), give the same solution, for a special but typical initial data forming finite time gradient blowup.

中文翻译：

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带有peakon-antipeakon初始数据的Camassa-Holm方程耗散解的唯一性

我们用一些peakon-antipeakon初始数据证明了Camassa-Holm方程耗散解的唯一性。我们的结果表明，通过Xin-Zhang在Xin and Zhang（2000）中消失的粘度方法和Bressan-Constantin在Bressan和Constantin（2007）中耗散溶液的坐标方法的转换，两个现有的全球存在框架给出了相同的结果。解决方案，用于形成有限时间梯度爆破的特殊但典型的初始数据。