Tomorrow-SISSA Math Phys Seminars
Donatella Iacono
iacono at sissa.it
Tue Jul 15 09:29:33 CEST 2008
Note the change of time.
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Geometry and Physics seminar
Wed 16 July 2008 12:00 - SISSA Room D
Dr. Vincenzo Sciacca (Palermo)
"Singularity formation for Prandtl's equations "
Abstract: Prandtl's equations for the impulsively started disk are
considered and solved using a spectral method in the streamwise direction
and finite--differences in the normal direction. The process of the
formation of the singularity is followed in the complex plane using the
singularity tracking method. The Van Dommelen and Shen's singularity is
classified as a cubic root singularity. We introduce a class of initial
data, defined as the superposition of the Van Dommelen and Shen solution
well before the appearance of their singularity plus an analytic
perturbation containing a particular complex singularity (that we call
dipole singularity). These data lead to an earlier singularity formation and
are uniformly bounded in norm $H^1$. The blow up time, which seems to be
possible to be taken short at will, behaves as the blow up time of the
Burger's equation with data in the same class. If in the Prandtl's equations
one restores the small viscosity in the streamwise direction one can see that
the behavior of the singularities is quite different. They stabilize at a
distance from the real axis which depends on the amount of the viscosity, and
the solutions remain regular. The physical meaning of the analytic
perturbation previously introduced is shown to be the placement of two
counter rotating vortices inside the boundary layer.
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For further information:
http://www.sissa.it/fm/seminars/seminars.php
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