Math.Koll. am 21.03.07/Prof. Schlag

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Wilhelm Schlag (University of Chicago)

mit dem Thema: ''Blowup phenomena for energy critical nonlinear wave
equations''

Abstract:
We will discuss singularity formation for energy critical nonlinear wave
equations. Our main concern will be the wave maps equation (also known as
sigma model) from 2+1 dimensions into S^2 and the semi-linear, quintic,
focusing wave equation  in 3+1 dimensions. These equations are locally
well-posed in the energy space, but it turns out that for large data blow-up
can occur. We will give particular examples of this phenomenon which entails
the bubbling-off of a stationary solution (for the wave maps equation this
is a harmonic map) with a prescribed rate of contraction. This latter
feature is somewhat unusual and is tied up with the fact that the linearized
equations (certain Schroedinger operators on the half-line) have a zero
enery resonances. This is joint work with Joachim Krieger (Harvard), and
Daniel Tataru (UCBerkeley).


Zeit: Mittwoch, 21. Maerz 2007, A C H T U N G !!! 16.00 Uhr (Kaffeejause),
anschlieszend 16.15 Uhr Vortrag

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
Seminarraum C 2.09

Harald Rindler
Gerald Teschl