Random perturbations of parabolic systems

In the deterministic regularity theory for parabolic systems, there are both classes of systems, where all weak solutions are actually more regular, and examples of systems which admit solutions that develop singularities in finite time. In this talk we investigate the regularity of solutions under the effect of random perturbations. On the one hand, we present an extension of a regularity result (due to Koshelev and Kalita) to the stochastic setting. On the other hand we discuss a partial result that might allow to attack the (open) question whether or not stochastic noise might even prevent the emergence of singularities for some particular systems.

(Joint work with F. Flandoli, Pisa)