ON A NEW 3D MODEL FOR INCOMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS  

作　　者：王术 

机构地区：[1]College of Applied Sciences, Beijing University of Technology [2]Institute of Mathematical sciences, Chinese University of Technology

出　　处：《Acta Mathematica Scientia》2010年第6期2089-2102,共14页数学物理学报（B辑英文版）

基　　金：supported by National Basic Research Program of China(973 Program, 2011CB808002);the NSFC (11071009);PHR-IHLB (200906103)

摘　　要：In this paper, we investigate some new properties of the incompressible Euler and Navier-Stokes equations by studying a 3D model for axisymmetric 3D incompressible Euler and Navier-Stokes equations with swirl. The 3D model is derived by reformulating the axisymmetric 3D incompressible Euler and Navier-Stokes equations and then neglecting the convection term of the resulting equations. Some properties of this 3D model are reviewed. Finally, some potential features of the incompressible Euler and Navier-Stokes equations such as the stabilizing effect of the convection are presented.In this paper, we investigate some new properties of the incompressible Euler and Navier-Stokes equations by studying a 3D model for axisymmetric 3D incompressible Euler and Navier-Stokes equations with swirl. The 3D model is derived by reformulating the axisymmetric 3D incompressible Euler and Navier-Stokes equations and then neglecting the convection term of the resulting equations. Some properties of this 3D model are reviewed. Finally, some potential features of the incompressible Euler and Navier-Stokes equations such as the stabilizing effect of the convection are presented.

关 键 词：finite time singularities nonlinear nonlocal system stabilizing effect of con- vection incompressible Euler and Navier-Stokes equations 

分 类 号：O357.1[理学—流体力学] O177.91[理学—力学]