Instructor: Stamatis Dostoglou

Description: The course will examine the Navier-Stokes equations of incompressible fluid motion and the barotropic and baroclinic equations of atmospheric motion from the point of view of infinite dimensional dynamical systems.

After presenting the usual themes of infinite dynamical systems (such as existence of attractors and invariant measures, methods of calculation of Hausdorff/fractal dimensions, Lyapunov exponents and Kolmogorov entropy) the course will examine their relation with physical quantities of the specific equations, such as vorticity/enstrophy, pressure etc.

The course will also insist on the predictive value of mathematical results and calculations that can be implemented using observed data.

References:

Doering, C. and J.D. Gibbon Applied Analysis of the Navier-Stokes equations Cambridge, 1995

Robinson, J. Inifnite-Dimensional Dynamical Systems: From Basic Concepts to Actual Calculations Cambridge, 2001

Majda, A. Introduction of the PDEs and Waves for the Atmosphere and the Ocean American Mathematical Society, 2003

Dymnikov V.P. and A.N. Filatov: Mathematics of Climate Modeling Birkauser 1997