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  

Existence and scaling limit of solutions of Leray-ɑmodel of three-dimensional Euler equations with transport noises

作　　者：龚园园 陈涌[1] GONG Yuanyuan;CHEN Yong(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学理学院,杭州310018

出　　处：《浙江理工大学学报（自然科学版）》2022年第6期931-940,共10页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：浙江省自然科学基金项目(LZJWY22E060002)。

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。In this paper,the transport noises were added to the deterministic Leray-ɑmodel and the Leray-ɑmodel of Euler equations with transport noises was constructed.The existence and scaling limit of solutions of the stochastic Leray-ɑmodel of Euler equations were studied in three-dimensional(3 D)space when transport noises tended to 0.Through Galerkin approximation and compactness method,we explored the existence of global weak solution(in the sense of distribution)of stochastic Leray-ɑmodel of Euler equations.In the meanwhile,the special value method was used to make the noise tend to 0,and the scaling limit of the solution was studied by combining Prohorov′s theorem and Skorokhod′s theorem.The results show that the solutions of Leray-αmodel of Euler equations with transport noises converge to the unique solution of the deterministic Leray-αmodel.This result solves the problem proposed by Barbato et al.of the scaling limit of the solution when the noise tends to zero.

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[理学—概率论与数理统计]