Recent Progress on Dynamic Stability and Global Regularity of 3D Incompressible Euler and Navier-Stokes Equations
主 题: Recent Progress on Dynamic Stability and Global Regularity of 3D Incompressible Euler and Navier-Stokes Equations
报告人: Prof.Thomas Y. Hou (California Institute of Technology )
时 间: 2009-10-09 下午14:00 - 15:00
地 点: 理科一号楼 1114(数学所活动)
Whether the 3D incompressible Euler and Navier-Stokes equations can
develop a finite time singularity from smooth initial data with finite energy has been one of the most long standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear
vortex stretching due to local geometric regularity of vortex filaments.
Our studies also reveal a surprising stabilizing effect of convection for the
3D incompressible Euler and Navier-Stokes equations. Finally, we present
a new class of solutions for the 3D Euler and Navier-Stokes equations, which
exhibit very interesting dynamic growth property.
By constructing a Lyapunov function which takes advantage of the cancellation between
the convection term and the vortex stretching term, we prove nonlinear stability and
the global regularity of this class of solutions.