Justifying the Thin Film Approximation: A Rigorous Limit Result for Stokes Flow driven by Surface Tension
Dr. Georg Prokert, Department of Mathematics and Computer Science, TU Eindhoven, Niederlande
In the moving boundary problem of Stokes flow driven by surface tension, we pass to the limit of small layer thickness. In an appropriate scaling, the limit evolution is given by the well- known Thin Film equation. While this is straightforward on the level of formal asymptotics, a rigorous analysis has to deal with the degeneracy of the limit which is reflected e.g. in the fact that a first-order evolution equation is replaced by a limit problem of order four. Our main techniques are uniform energy estimates in appropriately scaled Sobolev norms of sufficiently high order, based on parabolicity. This is joint work with M. Günther, Leipzig.
The Lecture is scheduled in Thursday, 6 May 2010, 14.30 in the seminar room of the Institute of Continuum Mechanics (Appelstr. 11, room A134).
