5 problems

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

The authors' conjecture. The observed power law is influenced by the limited small-scale separation accessible in the computations and would not occur under the assumptions conside…

Let $\rho$ be a passive scalar transported by a Sobolev vector field $u$, with initial datum $\rho_0$, and let $p$, $q$, and $r$ be the integrability exponents appearing in the pre…

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…

Scale-dependent diffusivity conjecture. If the scalings in the preceding relation hold, then