The Geometric Structure of Possible Singularities for the Navier-Stokes and Euler Equations

Speaker: Evan Miller

Date: Wed, Feb 16, 2022

Location: Online, PIMS

Conference: Emergent Research: The PIMS Postdoctoral Fellow Seminar

Subject: Mathematics

Class: Scientific


I will discuss several geometric constraints of the finite-time blowup of smooth solutions of the Navier-Stokes equation in the regularity criteria related to the eigenvalue structure of the strain matrix and to the vorticity direction. These regularity criteria suggest that strain self-amplification via axial compression/planar stretching drives any possible blowup. I will also discuss model equations where this form of blowup does indeed occur.

Speaker Biography:

Evan Miller received his PhD in mathematics from the University of Toronto under the supervision of Prof. Robert McCann in 2019. He was then a postdoc at McMaster University, working with Prof. Eric Sawyer. He was also a visiting postdoc at the Fields Institute in Toronto and the Mathematical Sciences Research Institute in Berkeley for thematic programs in mathematical fluid mechanics. At MSRI, he worked with Prof. Jean-Yves Chemin. Evan is now a PIMS postdoctoral fellow at the University of British Columbia working with Prof. Tai-Peng Tsai and Prof. Stephen Gustafson.