Stochastic cross-diffusion systems

We investigate the well-posedness of stochastic cross-diffusion systems. Such problems arise in many application areas like fluid dynamics of mixtures, cell biology and biofilm mmodeling. Cross-diffusion occurs if the gradient in the concentration of one species induces a flux of another species. Famous examples are given by the Maxwell-Stefan systems or bacterial biofilm models. The stochastic terms quantify the lack of knowledge of certain parameters or fluctuations which occur due to external perturbations. We explore a formal gradient-flow or entropy structure of these equations and an interplay between the entropy density and the stochastic terms in order to investigate properties of the solution.

This talk is based on a joint work with G. Dhariwal, F.Huber, A.Jüngel (Vienna University of Technology) and Christian Kuehn (Technical University of Munich).