The Hunter-Saxton equation with noise

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:270

Article

Holden, Helge¹  Karlsen, Kenneth H.²  Pang, Peter H. C.¹ 

[1] NTNU Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

[2] Univ Oslo, Dept Math, NO-0316 Oslo, Norway

关键词: Stochastic solutions;    Hunter-Saxton equation;    Nonlocal wave equations;    Wave-breaking;    Well-posedness;    Characteristics;   

DOI  :  10.1016/j.jde.2020.07.031

来源: Elsevier

【 摘 要 】

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. (C) 2020 The Authors. Published by Elsevier Inc.

【 授权许可】

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