Stochastic continuity equations with conservative noise

This talk is concerned with regularization by noise for the continuity equation. We will review the classical deterministic theory of Di-Perna/Lions and the regularization by linear, multiplicative noise initiated by Flandoli/Gubinelli/Priola. Finally, I will present a new result, joint with Benjamin Gess, which allows for non-linear, partially degenerate noise in conservative form.