Growth of Sobolev norms and loss of regularity in transport equations

Gianluca Crippa, Tarek Elgindi, Gautam Iyer +1

We consider transport of a passive scalar advected by an irregular divergence free vector field. Given any non-constant initial data $\bar{\rho }\in H_{\text{loc}}^1({\mathbb{R}}^d)$, $d\g…