2 problems

Weak Sard characterization. The vector field $v$ allows dissipation anomalies if and only if its stream function violates the weak Sard property.

Let $\theta^\kappa$ be a solution of the viscous transport equation on $\mathbb{T}^d$ with velocity field $u\in L^1([0,\infty),W^{1,1}(\mathbb{T}^d))$ and smooth initial data…