Scalar anomalous dissipation and optimal regularity via iterated homogenization

Jan Burczak, László Székelyhidi, Bian Wu

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