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BERLINER OBERSEMINAR Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)
WIAS Berlin, Humboldt-Universität zu Berlin
Prof. Dr. Th. Gallay (Université de Grenoble I, France)
Distribution of energy and convergence to equilibria in extended dissipative systems
Programm / Abstract:
We study the local energy dissipation in gradient-like nonlinear partial differential equations on unbounded domains. Our basic assumption, which happens to be satisfied in many classical examples, is a pointwise upper bound on the energy flux in terms of the energy dissipation rate. Under this hypothesis, we derive a simple and general bound on the integrated energy flux which implies that, in low space dimensions, our ``extended dissipative system'' has a gradient-like dynamics in a suitable averaged sense. In particular, we can estimate the time spent by any trajectory outside a neighborhood of the set of equilibria. As an application, we study the long-time behavior of solutions to the two-dimensional Navier-Stokes equation in an infinite cylinder. This talk is based on a collaboration with S. Slijepcevic (Zagreb, Croatia).
Zeit:
am Mittwoch den 05. Juni 2013 um 15:15
Ort:
Weierstraß-Institut
Mohrenstr. 39
10117 Berlin
Erhard-Schmidt-Hörsaal Erdgeschoss
eingetragen von kuphal(Olga.Kuphal@wias-berlin.de, 030 20372320)