Suppression of explosion by mixing

In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief introduction to the idea of mixing flow and the role it plays in the field of advection-diffusion-reaction equation, like the famous Keller-Segel equation for chemotaxis. More specifically, I will explain why the presence of fluid can enhance the dissipation and prevent the singularity formation for some types of evolution equations, even with degeneracy. I will also discuss different examples for mixing flow in this talk.