On the hydrostatic Euler equations: singularity formation, effect of rotation, and regularization by noise

Series
PDE Seminar
Time
Tuesday, February 4, 2025 - 3:30pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Quyuan Lin – Clemson University – quyuanl@clemson.eduhttps://sites.google.com/view/quyuanlin
Organizer
Gong Chen

The hydrostatic Euler equations, also known as the inviscid primitive equations, are derived from the Euler equations by taking the hydrostatic limit. They are commonly used when the aspect ratio of the domain is small, such as the ocean and atmosphere in the planetary scale. In this talk, I will first present the stability of finite-time blowup of smooth solutions to this model, then discuss the effect of fast rotation (from Coriolis force) in prolonging the lifespan of solutions. Finally, I will talk about the regularization effects that arise when the model is driven by certain random noise.