Global Well-posedness and Long-Term Dynamics for Certain Geophysical Models
Friday, February 15, 2002 - 11:00am - 12:00pm
The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, which are called the Primitive Equations, is often prohibitively expensive computationally, and hard to study analytically. In this talk I will present a formal derivation of more manageable shallow water approximate models for the three dimesional Euler equations in a basin with slowly spatially varying topography, the so called Lake Equation and Great Lake Equation, which should represent the behavior of the physical system on time and length scales of interest. These approximate models will be shown to be globally well-possed. I will also show that the Charney-Stommel model of the gulf-stream, which is a two dimensional damped driven shallow water model for ocean circulation, has a global attractor. Whether this attractor is finite or infinite dimensional is still an open question. Other results concerning the global well-posedess of three dimensional viscous planetary geostrophic models will be presented.