Session:Stochastic Partial Differential Equations<br>Organizer:

Saturday, August 6, 2005 - 3:45pm - 5:30pm
EE/CS 3-180
Jonathan Mattingly (Duke University)
  • Stochastic modulation equations
    Martin Hairer (University of Warwick)
    We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. Unlike in the deterministic case, this approximation holds for all times and extends to the respective invariant measures.
  • Ergodicity of the degenerately forced stochastic fluid equations
    Jonathan Mattingly (Duke University)
    I will present a theory which allows one to prove the uniqueness of the stationary measure for a large class of SPDEs with additive noise. To do so, I will discuss Malliavin Calculus in the SPDE setting and a generalization of Hormander's hypo-elliptic theory to the SPDEs. I will also discuss a new generalization of the strong Feller property which seems to be use full in infinite dimensions.
  • On the foundation of the Lp-theory of SPDEs

    We discuss a detailed proof of a generalization of the Littlewood-Paley inequality upon which the Lp-theory of SPDEs is based.