Stochastic 3D Leray-α model with fractional dissipation  

作　　者：Shihu Li Wei Liu Yingchao Xie 

机构地区：[1]School of Mathematics and Statistics/Research Institute of Mathematical Science,Jiangsu Normal University,Xuzhou 221116,China

出　　处：《Science China Mathematics》2023年第11期2589-2614,共26页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12001247);supported by National Natural Science Foundation of China(Grant Nos.12171208,11831014 and 12090011);supported by National Natural Science Foundation of China(Grant Nos.11931004 and 12090011);Natural Science Foundation of Jiangsu Province(Grant No.BK20201019);the Priority Academic Program Development of Jiangsu Higher Education Institutions。

摘　　要：In this paper,we establish the global well-posedness of the stochastic 3D Leray-αmodel with general fractional dissipation driven by multiplicative noise.This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of orderθ1 in the nonlinear term and theθ2-fractional Laplacian.In the case ofθ1≥0 andθ2>0 withθ1+θ2≥5/4,we prove the global existence and uniqueness of strong solutions.The main results not only cover many existing works in the deterministic cases,but also generalize some known results of stochastic models such as the stochastic hyperviscous Navier-Stokes equations and classical stochastic3D Leray-αmodel as the special cases.

关 键 词：stochastic Leray-Q model fractional Laplacian stochastic Navier-Stokes equation WELL-POSEDNESS 

分 类 号：O211.6[理学—概率论与数理统计]