|本期目录/Table of Contents|

[1]龚园园,陈涌.带有输运型噪声的三维Euler型Leray-ɑ模型解的存在性及极限行为[J].浙江理工大学学报,2022,47-48(自科六):931-940.
　GONG Yuanyuan,CHEN Yong.Existence and scaling limit of solutions of Leray-ɑ model of three dimensional Euler equations with transport noises[J].Journal of Zhejiang Sci-Tech University,2022,47-48(自科六):931-940.
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带有输运型噪声的三维Euler型Leray-ɑ模型解的存在性及极限行为()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第47-48卷
期数:
2022年自科第六期
页码:
931-940
栏目:
出版日期:
2022-11-10

文章信息/Info

Title:
Existence and scaling limit of solutions of Leray-ɑ model of three dimensional Euler equations with transport noises
文章编号:
1673-3851 (2022) 11-0931-10
作者:
龚园园; 陈涌
浙江理工大学理学院，杭州 310018
Author(s):
GONG Yuanyuan;  CHEN Yong
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
随机Euler型Leray-ɑ模型; 输运型噪声; Prohorov定理Skorokhod 定理;  Galerkin 逼近方法; 紧性方法
分类号:
O211-63
文献标志码:
A
摘要:
在确定性Leray-ɑ模型上添加输运型噪声，构造带有输运型噪声的Euler型Leray-ɑ 模型，研究在三维情况下输运型噪声趋于0时该随机Euler型Leray-ɑ模型解的存在性及极限行为。通过Galerkin逼近和紧性方法，探究随机Euler型Leray-ɑ模型在分布意义下整体弱解的存在性；利用取特殊值的方法，使噪声趋于0，结合Prohorov定理和Skorokhod定理探究其解的极限行为。研究结果表明：带有输运型噪声的Euler型Leray-ɑ模型的解是收敛到确定性Leray-ɑ模型的唯一解。该结果解答了Barbato等提出噪声趋于0时解的极限行为问题。

参考文献/References:

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［7］Flandoli F, Galeati L, Luo D J. Delayed blow-up by transport noise［J］. Communications in Partial Differential Equations, 2021, 46(9): 1757-1788.

［8］Flandoli F, Gubinelli M, Priola E. Well-posedness of the transport equation by stochastic perturbation［J］. Inventiones Mathematicae, 2010, 180(1): 1-53.

［9］Luo D J. Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system［J］. Nonlinearity, 2021, 34(12): 8311-8330.

［10］Luo D J, Zhu R C. Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit［J］. Stochastic Processes and Their Applications, 2021, 140: 236-286.

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备注/Memo

备注/Memo:
收稿日期： 2022-06-10
网络出版日期：2022-09-06
基金项目： 浙江省自然科学基金项目(LZJWY22E060002)
作者简介： 龚园园(1997-)，女，安徽颍上人，硕士研究生，主要从事随机偏微分方程方面的研究
通信作者： 陈涌，E-mail：chenyong@zstu.edu.cn
更新日期/Last Update: 2022-11-07