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W. G. Pritchard Lab Seminar: 11:15 AM - 12:15 PM, 106 McAllister Bldg
**Monday October 16, 2006**
Twist & Shout: Maximal Enstrophy Production in the 3D Navier-Stokes
Equations
Charles R. Doering
Dept of Mathematics
University of Michigan
Abstract:
It's still an open question whether solutions to the 3D Navier-Stokes
equations for incompressible flows in a finite periodic box can become
singular in finite time. It is known, however, that as long as the
enstrophy (the mean-square vorticity) of a solution remains finite, the
solution remains smooth. The generation rate of enstrophy is given by a
functional that can be bounded using elementary functional estimates.
Those estimates establish short-time regularity but do not rule out
finite-time singularities in the solutions. We formulate and solve the
variational problem for the maximal growth rate of enstrophy, and display
flows that generate enstrophy at the greatest possible rate. The results
are discussed in the context of the search for either regularity or
singularity in solutions of the 3D Navier-Stokes equations. This is joint
work with Lu Lu.
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