Transport, mixing, and fluids (6/6)

by Prof. Gianluca Crippa (Universität Basel)

Wednesday 9 Jun 2021, 09:00 → 11:00 Europe/Rome

GSSI

Transport, mixing, and fluids

 

GSSI, May 31 - June 9, 2021 (12 h)

 

 

1) The continuity equation and the flow of a vector field.

2) Mixing and mixing scales (geometric and analytical).

3) Lower bounds on the mixing scales for Lipschitz vector fields.

4) A short introduction to the DiPerna-Lions theory.

5) Energy estimates and (non optimal) lower bounds for the analytical mixing scale.

6) Mild regularity of the regular Lagrangian flow.

7) Exponential lower bound for the geometric mixing scale.

8) Exponential lower bound for the analytic mixing scale.

9) Scaling analysis in self-similar evolutions.

10) Optimality of the exponential lower bounds.