Large deviations from porous media and gradient flow structures

We consider the large deviations of the rescaled zero range process about its hydrodynamic limit. This leads to the analysis of the skeleton equation, a degenerate parabolic-hyperbolic PDE with irregular drift. In this talk, we present a robust well-posedness theory for such PDEs in energy-critical spaces based on concepts of renormalized solutions and the equation’s kinetic form. The relation of such large deviations to a formal gradient flow interpretation of the porous medium equation will be drawn by deducing an entropy dissipation equality from the large deviations and reversibility. 

The talk will be followed by refreshments in the common room at 4pm.