BCAM Alumni & Former Members Seminar: A few mathematical questions on the dynamics of non-homogeneous fluids

LOCATION: Maryam Mirzkhani Seminar room at BCAM | 12:00 p.m.

Title
A few mathematical questions on the dynamics of non-homogeneous fluids

Abstract
In this talk, we deal with some systems of PDEs which describe the motion of geophysical flows. From the physical standpoint, these are flows whose dynamics takes place at very large scales and is mainly influenced by the rotation of the Earth and by the action of gravity. The physical processes involved in the dynamics of geophysical flows are many and, by now, quite well understood: for instance,
dimensional reduction, stratification in density, boundary layer formation and related effects, propagation of waves.

By giving an overview of results obtained on systems of increasing order of complexity, we aim at showing how, and to which extent, it is possible to capture in a rigorous way the previous phenomena in the mathematical models. In passing, we explain also how rigorously deriving simplified models for geophysical fluid dynamics, starting from more complex primitive equations, by using tools from asymptotic analysis. Our main focus is to discuss effects linked with variations of the fluid density and to explain how to handle the presence of multiple scales in the model.