The Hunter-Saxton equation with noise
Analysis of PDEs
2022-10-18 v1
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.
Keywords
Cite
@article{arxiv.2003.13984,
title = {The Hunter-Saxton equation with noise},
author = {Helge Holden and Kenneth H. Karlsen and Peter H. C. Pang},
journal= {arXiv preprint arXiv:2003.13984},
year = {2022}
}