Well-posedness of the Dean-Kawasaki equation with correlated noise
A talk in the Bielefeld Stochastic Afternoon series by
Benjamin Fehrman
| Abstract: | This talk can be joined in the common room (V3-201) or via Zoom (for details email stochana(at)math.uni-bielefeld.de).
The Dean-Kawasaki equation, and more generally certain singular stochastic PDEs with conservative space-time white noise, arise formally in fluctuating hydrodynamics and macroscopic fluctuation theory to describe far from equilibrium behavior in physical systems---such as the fluctuations of an interacting particle system about its hydrodynamic limit. The treatment of these SPDEs presents a significant mathematical challenge, due both to their supercriticality and their degenerate and singular coefficients.
In this talk, which is based on joint work with Benjamin Gess, I will discuss a well-posedness theory for such equations with correlated noise. The introduction of smooth noise is justified by the fact that discrete microscopic systems often have a natural correlation scale---such as the grid-size---and by the fact that, along appropriate scaling limits, we prove that the solutions accurately describe the particle system in terms of a law of large numbers, central limit theorem, and large deviations principle. The methods treat general nonlinearities that are only locally 1/2-Hölder continuous, and solve several open problems including the well-posedness of the Dean-Kawasaki and nonlinear Dawson-Watanabe equations with correlated noise. Within the CRC this talk is associated to the project(s): B8 |