Special Session 35: 

Stochastic continuity equations with conservative noise

Scott Smith
University of Wisconsin-Madison
USA
Co-Author(s):    Benjamin Gess
Abstract:
I will discuss the continuity equation with non-linear and partially degenerate stochastic perturbations in divergence form. Our main result uses the noise to avoid concentrations in the density under weaker hypotheses on the driving velocity field than in the deterministic setting. In comparison with related results involving linear multiplicative noise, our proof makes use of the regularity theory for fully non-linear parabolic equations.