Can the behaviour of microscopic stochastic systems give insight into analysis of upscaled PDEs?  (part 2)

Abstract

The last talk dealt with building an understanding of gradient flows, and reflected on two crucial properties: (1) gradient flows have a natural (variational) structure, and (2) this variational structure has connections to large deviations.

The second talk will focus on building upon the second connection. In particular, using the example of the kinetic Fokker-Planck equation, I will present a large-deviation inspired variational form for this equation. Furthermore, I will show that this variational form naturally meshes with studying singular limit problems due to the various a priori estimates available for such structures.