Selected topics in transport phenomena: deterministic and probabilistic aspects

Well-posedness and regularization by noise for scalar conservation laws

Benjamin Gess

Max Planck Institute for Mathematics in the Sciences


In this talk we will revisit regularizing effects of noise for nonlinear SPDE. In this regard we are interested in phenomena where the inclusion of stochastic perturbations leads to increased regularity of solutions as compared to the unperturbed, deterministic case. Closely related, we study effects of production of uniqueness of solutions by noise, i.e. instances of nonlinear SPDE having a unique solution, while non-uniqueness holds for the deterministic counterparts. The talk will concentrate on these effects in the case of nonlinear scalar conservation laws and stochastic porous media equations.