BCAM SO Course | Introduction to the mathematical theory of incompressible fluids

Funding request: Dec 22 2023 |

Registration start: Nov 12 2023 | 

Registration deadline: Feb 09 2024 | Online Registration deadline on February 21, 2024

The present course is intended to be an introduction, for master and Ph.D. students, to the mathematical theory of fluid dynamics. The course will focus on incompressible fluids and is composed of two main parts. The first one will be about ideal flows, namely homogeneous flows for which viscous dissipation effects are neglected. The second one, instead, will treat the theory of viscous (still homogeneous) fluids. Some more advanced results will be presented at the end of the course, about the equations of Magnetohydrodynamics.

The main goal of the course is twofold. On the one hand, this course wants to give an overview of classical results on the study of continuum mechanics, in order to motivate students who could have an interest in such a topic. On the other hand, through that study, the course aims at giving students a solid mathematical background on theoretical tools of linear and non-linear analysis which are relevant in the study of partial differential equations.

PREREQUISITES

• L^p spaces, Sobolev spaces.
• Basics of functional analysis: Banach and Hilbert spaces, weak topologies etc.
• Distribution theory.
• Fourier transform, tempered distributions, Sobolev spaces of fractional order.