论文标题
带有噪音的猎人 - 萨克斯顿方程
The Hunter-Saxton equation with noise
论文作者
论文摘要
在本文中，我们为随机的猎人 - 萨克斯顿等等开发了凯奇问题的存在理论，并证明了其解决方案的爆炸的几种特性。本文的一个重要部分是延续了解决随机方程以外的随机方程（波浪破坏）。在线性噪声案例中，使用（随机）特征的方法，我们还研究了确定性问题中未观察到的随机波动和随机效应。值得注意的是，我们在随机的波浪时间中得出了明确的定律。
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter-Saxton equatio, and prove several properties of the blow-up of its solutions. An important part of the paper is the continuation of solutions to the stochastic equations beyond blow-up (wave-breaking). In the linear noise case, using the method of (stochastic) characteristics, we also study random wave-breaking and stochastic effects unobserved in the deterministic problem. Notably, we derive an explicit law for the random wave-breaking time.
