## Department Colloquium

### Friday, March 13th, 2020

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Tai-Peng Tsai (University of British Columbia)

**Title:** Discretely self-similar solutions of incompressible Navier-Stokes equations and the local energy class.

**Abstract: ** In this talk, we first review several concepts of solutions of the incompressible Navier-Stokes equations and the questions of regularity and uniqueness. We then introduce forward and backward self-similar solutions and their variants, and the similarity transform. We next sketch a few constructions of forward discretely self-similar (DSS) solutions for arbitrarily large initial data in weak $L^3$ and $L^2$ local. We finally explain their connection to the theory of local energy solutions.

**Tai-Peng Tsai** graduated from the University of Minnesota under the supervision of Vladimir Sverak. He was a Courant Instructor at the New York University and a Member of the Institute for Advanced Study before he joined the University of British Columbia. He works on the analysis of fluid and dispersive PDEs, including the regularity problem and self-similar solutions of Navier-Stokes equations, the asymptotic behavior of multi-solitons of Schrödinger and gKdV equations, and the regularity of energy critical Schrödinger maps.