The Hunter-Saxton equation with noise
Peer reviewed, Journal article
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Date
2021Metadata
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- Institutt for matematiske fag [2350]
- Publikasjoner fra CRIStin - NTNU [37177]
Abstract
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter–Saxton equation (1.1), 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.