16 dec 2004

Abstract.

Seminario di Analisi Analysis Seminar

when: Giovedì 16 dicembre, ore 17.00 Thursday, december 16, at 5 pm:

where: Dipartimento di Matematica, aula magna

speaker: Frederic Charve (Ecole Polytechnique, Paris)

title: Asymptotics for a geophysical fluids system: study of dispersion phenomena induced by strong rotation and stratification

abstract: After a small explanation of the characteristics of geophysical fluids, rotation of the earth and vertical stratification of the density, we will write the system of the primitive equations. We will first formally obtain the limit system (called the quasigeostrophic system) and give a first explanation of the problem of getting the limit when \varepsilon goes to zero. Then we will talk about oscillations and dispersion for the wave equation. After a study of the eigen elements of the linearized system we will get dispersive estimates and Strichartz estimates. In application of these Strichartz estimates we obtain the asymptotics in the case of weak solutions (Leray solutions), strong solutions (in the sense of Fujita-Kato). We then give much more precise estimates for the speed of convergence and also in the case of regular vortex patches.