[Mathmajors] Lecture by Tom Hou on Thursday, 2/12

[Julie Martinson]

Boeing Distinguished Colloquium in Applied Mathematics
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Please join us for the next talk in this series and the
reception afterwards.  More info and pictures:
    http://www.amath.washington.edu/events/boeing


Speaker:  Thomas Hou, Caltech
Title:    Recent Progress on Dynamic Stability and Global Regularity
           of 3D Incompressible Euler and Navier-Stokes Equations

Time:     4pm on Thursday, February 12, 2009
Place:    Guggenheim 220 (the Auditorium)

Abstract:

Whether the 3D incompressible Navier-Stokes equations can develop
a finite time singularity from smooth initial data is one of the
seven Millennium Open Problems posted by the Clay Mathematical
Institute. We review some recent theoretical and computational
studies of the 3D Euler equations which show that there is a
subtle dynamic depletion of nonlinear vortex stretching due to
local geometric regularity of vortex filaments. The local geometric
regularity of vortex filaments can lead to tremendous cancellation
of nonlinear vortex stretching, thus preventing a finite time
singularity. 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 exploiting the special structure of the
solution and the cancellation between the convection term and the
vortex stretching term, we prove nonlinear stability and the global
regularity of this class of solutions.

Thomas Hou is the Charles Lee Powell Professor and Executive
Officer of Applied and Computational Mathematics at the California
Institute of Technology. Professor Hou has won numerous awards
including the Sloan Fellowship (1990-1992), the Feng Kang Prize
in Scientific Computing (1997), the APS Francois N. Frenkiel Award
(1998), the SIAM James H. Wilkinson Prize in Numerical Analysis and
Scientific Computing (2001), the Morningside Gold Medal in Applied
Mathematics, International Congress of Chinese Mathematicians (2004),
and the Computational and Applied Sciences Award, the United States
Association of Computational Mechanics (2005). In addition, he is
on numerous editorial boards including as the founding editor of
the SIAM Journal on Multiscale Modeling and Simulation.

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Coming Attractions in this series:

February 26, 2009: Carl Bender, Washington University
Quantum Mechanics in the Complex Domain

April 9, 2009:  Marty Golubitsky, Ohio State University

May 7, 2009:  Phil Holmes, Princeton University

May 21, 2009: Nick Trefethen, Oxford University


Walker Ames Lecture:

April 9, 2009 at 6:30pm: Michael Mackey, McGill University
Bifurcations at the Bedside: How Non-Linear Dynamics Can Help to
Understand Periodic and Dynamical Disease

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To sign up for future announcements of this series and other talks:
    https://mailman1.u.washington.edu/mailman/listinfo/amath-seminars


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Randall J. LeVeque                  |   rjl at washington.edu
University of Washington            |   phone: 206-685-3037
Department of Applied Mathematics   |   fax:   206-685-1440
Box 352420                          |   office: Guggenheim 415C
Seattle, WA  98195-2420             |   www.amath.washington.edu/~rjl/
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