The Hunter-Saxton equation with noise
arXiv:2003.13984 · doi:10.1016/j.jde.2020.07.031
Abstract
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.
Cited by in corpus (4)
- Uniqueness of conservative solutions for the Hunter-Saxton equation
- Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
- Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities
- Strong solutions of a stochastic differential equation with irregular random drift