## Nonlinear Partial Differential Equations

**Date: ** March 21, 2023

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **Xin Liu, Texas A&M University

**Title: ***A revisit to the rigorous justification of the quasi-geostrophic approximation *

**Abstract: **The quasi-geostrophic approximation is used to model large-scale atmospheric/oceanic flows closed to the geostrophic balance, i.e., the Coriolis force, the pressure, and the gravity are in balance. Such an approximation for inviscid flows has been investigated in the case without boundary or without oscillating fast waves. In this talk, I will (1) review the classical mathematical results of the QG approximation, (2) point out the possible boundary layer when fast rotation is not present, and (3) show that with fast rotation, there is not boundary layer. In particular, we rigorously justify the QG approximation with both boundary and oscillating fast waves. This is done by introducing a new generalized potential vorticity, obtaining uniform estimates, and passing the weak limit. Our result demonstrates the stabilizing effect of rotation by suppressing the boundary layer. This is joint work with C. Bardos and E. Titi.