The Hunter-Saxton equation with noise

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.

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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