Scalar anomalous dissipation and optimal regularity via iterated homogenization

Jan Burczak, László Székelyhidi, Bian Wu

For any ${\hat{I}}_0^2<1/3$ we construct divergence free vector fields in $C_{x,t}^{{\hat{I}}_0^2}$ and a sequence of diffusivities $\hat{I}{º}_q\searrow 0$ such that, for an arbitrary initial datum from…