Work

The Hunter–Saxton equation with noise

Year: 2020

Type: article

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.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2020.07.031

Authors: Helge Holden, Kenneth H. Karlsen, Peter H.C. Pang

Institutions: Norwegian University of Science and Technology, University of Oslo

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,600

Funder: Norges Forskningsråd