In this talk I will describe a recent work of Isett-Vicol on weak solutions to the active scalar equation $\partial _t \theta + \nabla \cdot (u \theta ) = 0$, where $u = T[\theta ]$ is a divergence-free velocity field given in terms of a Fourier multiplier $T$ applied to θ. An emphasis will given on the phenomenon of `rigidity vs. flexibility': Depending on whether the symbol for $T$ is odd...