Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (6): 2089-2102.doi: 10.1016/S0252-9602(10)60193-2

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

 WANG Shu   

  1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, China and Institute of Mathematical sciences, Chinese University of Technology, Hong kong, China
  • Received:2010-09-18 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    The research was supported by National Basic Research Program of China (973 Program,  2011CB808002), the  NSFC (11071009) and PHR-IHLB (200906103).

Abstract:

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.

Key words: finite time singularities, nonlinear nonlocal system, stabilizing effect of convection, incompressible Euler and Navier-Stokes equations

CLC Number: 

  • 35C20
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