## Applied Mathematics Colloquium: Dr Gautam Iyer

#### Carnegie Mellon University

Friday, October 29, 2021 · 2 - 3 PM

Dissipation Enhancement, Mixing and Blow-up Suppression

Diffusion and mixing are two fundamental phenomena that arise in a wide

variety of applications. In this talk we quantitatively study the

interaction between diffusion and mixing in the context of problems

arising in fluid dynamics. The first question we address is how fast the

energy can decay in the advection diffusion equation. Even though this

is a simple linear equation, the energy decay rate is intrinsically

related to the mixing properties of the advecting velocity field, and

there are many unresolved open questions. I will present a few recent

results involving both upper and lower bounds, and then consider

applications to studying the long time dynamics of a few model

non-linear equations arising in chemotaxis and phase separation.

Diffusion and mixing are two fundamental phenomena that arise in a wide

variety of applications. In this talk we quantitatively study the

interaction between diffusion and mixing in the context of problems

arising in fluid dynamics. The first question we address is how fast the

energy can decay in the advection diffusion equation. Even though this

is a simple linear equation, the energy decay rate is intrinsically

related to the mixing properties of the advecting velocity field, and

there are many unresolved open questions. I will present a few recent

results involving both upper and lower bounds, and then consider

applications to studying the long time dynamics of a few model

non-linear equations arising in chemotaxis and phase separation.