Mathematics Graduate Student Colloquium

Analytical Study of Multi-Layer and Continuously Stratified Barotropic Models of Ocean Dynamics

Aseel Farhat
Friday, May 4, 2012
4:00 pm - 4:50 pm
RH440R

Talk Abstract:

In geophysics, multilayer models are derived under the assumption that the fluid consists of a finite number of homogeneous layers of distinct densities. We introduce a two-layer model that was derived to study the perturbation about a vertical shear flow. We show that the model is linearly unstable, however the solutions of the nonlinear model are bounded in time. We prove the existence of finite dimensional compact attractor and derive upper bounds on its dimension.

In plasma physics, the 3D Hasegawa-Mima equation is one of the most fundamental models that describe the electrostatic drift waves. In the context of geophysical fluid dynamics, the 3D Hasegawa- Mima equation appears as a simplified model of a reduced Rayleigh-Bénard convection model that describes the motion of a fluid heated from below. Investigating the 3D Hasegawa-Mima model is challenging even though the equations look simpler than the 3D Euler equations. Inspired by these models, we introduce and study a simplified mathematical model that has a nicer mathematical structure. We prove the global existence and uniqueness of solutions of the 3D simplified model as well as a continuous dependence on the initial data result. These results are one of the first results related to the 3D Hasegawa-Mima equation.

About the Speaker:

Aseel will be a Zorn Postdoctoral Fellow at Indiana University this fall. She enjoys flashy earrings and has an impressive collection of shoes.

Advisor and Collaborators

Edriss Titi is currently Aseel's advisor.

Supplementary Materials:

none

Refreshments:

Pizza will be served after the talk.

Last Modified: November 07, 2012 at 9:54 PM (UTC)
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