Event Detail

Event Type: 
Analysis Seminar
Monday, November 8, 2021 - 12:00 to 12:50
KIDD 238

Speaker Info

Institute for Advanced Study

We consider the evolution of a passive scalar (for example, a temperature distribution) which is transported by a fluid flow and diffuses. We focus on two aspects of the corresponding advection-diffusion PDE. First, it is well known that shear in the background flow may interact with the diffusion to cause the solution to decay faster than it would by diffusion alone. This so-called enhanced dissipation has been widely studied in the PDE community over the past two decades. We revisit this phenomenon from the new but old perspective of Hormander's classical work on hypoellipticity. This is joint work with Rajendra Beekie (NYU) and Matthew Novack (IAS). Second, we determine sharp conditions on the divergence-free drift for quantitative local boundedness, Harnack's inequality, and pointwise upper bounds on fundamental solutions to hold. This is joint work with Hongjie Dong (Brown).