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.
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.
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)
