Global Cauchy Problem for a Leray-α Model

作     者：Hua QIU Yi DU Zheng-an YAO 

作者机构：Department of Applied Mathematics South China Agricultural University Guangzhou 510642China Department of Mathematics Jinan University Guangzhou 510632 China E-mail: School of Mathematics Sun Yat-Sen University Guangzhou 510275 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2017年第33卷第1期

页      面：207-220页

核心收录：

学科分类：080704[工学-流体机械及工程] 07[理学] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11126266,11471126 and 11431015) the Natural Science Foundation of Guang Dong Province(Grant No.2016A030313390) the China 973Program(Grant No.2011CB808002) 

主　　题：Leray-α model Cauchy problem Littlewood-Paley decomposition global well-posedness 

摘      要：In this paper, we consider the Cauchy problem for the 3D Leray-α model, introduced by Cheskidov et al.[11]. We obtain the global solution for the 3D Leray-α model in the fractional index Sobolev space, and prove that the 3D Leray-α model reduces to the homogeneous incompressible Navier-Stokes equations as α↓0＋, and the solution of the 3D Leray-α model will converge to the weak solution of the corresponding Navier-Stokes equations.