Anna Mazzucato

Penn State University

Optimal mixing in incompressible flows

I will discuss transport of passive scalars by incompressible flows (such as ink in water) and measures of optimal mixing and stirring. In particular, I will present recent results concerning examples of flows that achieve the optimal mixing rate, when the flow satisfies certain physical constraints, such as an energy or a power budget, expressed as bounds on Sobolev norms of the velocity field.

I will give two applications, one is an example of complete loss of regularity for solution to linear transport equations, the other is a global existence result for the advective Kuramoto–Sivashinsky equation in 2 space dimensions.