Noise effect in a stochastic generalized Camassa-Holm equation

Autor:	Yingting Miao, Zhenzhen Wang, Yongye Zhao
Rok vydání:	2022
Předmět:	Applied Mathematics General Medicine Analysis
Zdroj:	Communications on Pure and Applied Analysis. 21:3529
ISSN:	1553-5258 1534-0392
DOI:	10.3934/cpaa.2022113
Popis:	In this paper we consider a stochastic variant of the generalized Camassa-Holm equation. We first establish some local results, including local existence, uniqueness and a blow-up criterion characterizing the possible blow-up of the solutions, for the corresponding stochastic partial differential equation. Then we study the effect of noise. For the relatively small noise, in terms of the dependence on initial data, we construct an example to show that the SPDE is weakly instable in the sense that either the exiting time is not strongly stable, or the dependence on initial data is not uniformly continuous. Finally, for the large noise, we prove that singularities can be prevented, i.e., large noise has regularization effect.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::715c8ef3cd44fe2d5ac3079d385fe6eb https://doi.org/10.3934/cpaa.2022113 Zobrazit plný text záznamu