CRM: Centro De Giorgi
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Stochastic Fluid Mechanics and SPDEs

seminar: Stochastic Dynamics near a Bifurcation - Amplitude Equations

speaker: Dirk Blömker (University of Augsburg )

abstract: Noise, for instance induced by thermal fluctuations, is natural in many physical models like the Rayleigh-Bénard convection. Near the convective instability, one can use the natural separation of time-scales for a multi-scale analysis, in order to derive amplitude equations. These are simpler equations, but they describe the essential dynamics of the system. We discuss how noise enters these equations. As an example, we consider in this talk the stochastic Swift-Hohenberg equation, which is the toy model for convection problems. We give rigorous error estimates for the approximation via amplitude equations. This extends to long time behaviour given by invariant measures, and has applications in pattern formation below the threshold of instability.

Fri 28 Jul, 11:10 - 11:50, Aula Dini
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