Geophysikalisches Kolloquium: Mathematical Study of Certain Geophysical Models

The basic problem faced in geophysical fluid dynamics is that a mathematical description based only on fundamental physical principles, the so-called "Primitive Equations'', is often prohibitively expensive computationally, and hard to study analytically. In this talk I will survey the main obstacles in proving the global regularity for the three-dimensional Navier-Stokes equations and their geophysical counterparts. However, taking advantage of certain geophysical balances and situations, such as geostrophic balance and the shallowness of the ocean and atmosphere, geophysicists derive more simplified and manageable models which are easier to study analytically. In particular, I will present the global well-posedness for the three-dimensional Benard convection problem in porous media, and the global regularity for a three-dimensional viscous planetary geostrophic models. Furthermore, these systems will be shown to have finite dimensional global attractors.

Even though the Primitive Equations look as if they are more difficult to study analytically than the three-dimensional Navier-Stokes equations I will show in this talk that they have a unique global (in time) regular solution for all initial data.

This is a joint work with Chongsheng Cao.

Date

24.05.2012

Time

15:15 h

Place

Geomatikum H1
Lecture Hall H1 (ground floor), University of Hamburg, Bundesstr. 55, Hamburg

Speaker

Edriss S. Titi, University of California, Irvine; Department of Mathematics, Mechanical and Aerospace Engineering

Organizers

Peter Korn

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