Winter 2026
Time: Fridays, 2pm-3pm, Pacific time
Location: Hybrid - South Hall 4607 and in Zoom (link provided upon request)
Please contact Mingsong Yan (mingsongyan@ucsb.edu), Qirui Peng (qpeng9@ucsb.edu), Ruimeng Hu (rhu@ucsb.edu), or Sui Tang (suitang@ucsb.edu) to reserve a slot.
Upcoming Seminar Schedule:
(Click the event below to see the title and abstract)
Title: Weak uniformly local L^2 solutions to the 2D Quasi-geostrophic Equations
Abstract: The surface quasi-geostrophic (SQG) equation is a fundamental model in fluid dynamics that describes how temperature variations on the surface of a rotating fluid (like the atmosphere or ocean) can influence motion. In this talk, we study both the inviscid (no friction) and α-dissipative (with fractional diffusion) versions of this equation, collectively known as the α-SQG equations. To better understand these models, we first introduce a related system called the Double Dissipative SQG (DSQG) equations and show that solutions to this system behave nicely under certain conditions. We then investigate what happens as the effects of viscosity (or dissipation) become very small—a process known as taking the inviscid limit. Using energy estimates, we prove that solutions remain stable and converge as this limit is taken. Finally, we show that the limiting solution satisfies the weak form of the α-SQG equation, and with enough smoothness, it becomes a classical solution. Throughout, I’ll give an overview of the mathematical tools involved and explain how these results contribute to our broader understanding of fluid motion and turbulence models.
Host: Michael Gulas