论文标题
使用Pearmon-Antipeakon初始数据的Camassa-Holm方程的耗散溶液的独特性
Uniqueness of Dissipative Solution for Camassa-Holm Equation with Peakon-Antipeakon Initial Data
论文作者
论文摘要
我们为Camassa-Holm方程的耗散解决方案提供了证明，并在Dafermos早先在Hunter-Saxton方程中[5]中重新释放了一些Pearmon-Antipeakon初始数据。我们的结果表明，通过Xin-Zhang在[11]中的消失的粘度方法以及[3]中Bressan-Constantin耗散解决方案的坐标方法的转换，提供了相同的解决方案，以提供相同但典型但典型的初始数据形成有限的时间梯度爆炸。
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.
