Growth of Sobolev norms and loss of regularity in transport equations
Growth of Sobolev norms and loss of regularity in transport equations
We consider transport of a passive scalar advected by an irregular divergence-free vector field. Given any non-constant initial data [Formula: see text], [Formula: see text], we construct a divergence-free advecting velocity field [Formula: see text] (depending on [Formula: see text]) for which the unique weak solution to the transport equation …