Abstract. I will discuss transport of passive scalars by incompressible flows and measures of optimal mixing and stirring. I will present two examples of opposite effects of mixing: one leads to irregular transport and a dramatic, instantaneous loss of regularity for transport equation, the other is enhanced dissipation, which can lead to global existence in non-linear, dissipative systems. In particular, I will show how mixing leads to global existence for the 2D Kuramoto-Sivashisky equation, a model for flame propagation.



Bio. Anna Mazzucato is Professor of Mathematics and Distinguished Senior Scholar in the Eberly College of Science at Penn State University in the USA, where she is the Associate Head of Administration in the Mathematics Department. She works in applied analysis and partial differential equations with applications to continuum mechanics and inverse problems.Prior to joining Penn State in 2003, she was a Gibbs Instructor at Yale University and a Postdoctoral Fellow at the IMA and MSRI. She obtained her PhD from the University of North Carolina-Chapel Hill in 2000 under the direction of Micheal Taylor. In 2011 she received the Ruth I. Michel Memorial Prize from the AWM and Cornell University and was elected SIAM Fellow in 2021.She has authored over 50 publications and has served the mathematics community in several capacities. In particular, she is the current Chair of the AMS Editorial Boards Committee and serves on the editorial boards of several major journals, including Analysis & PDE, Physica D, and SIAM Journal on Mathematical Analysis. She has been continuously supported by grants from the US National Science Foundation since 2004.