Winter 2025, Math 444/550 (Topics in fluid dynamics)
Topic: Fundamental models in fluid dynamics
Professor:
David Goluskin
Course description:
The course will be an introduction to the behaviour of fluids (liquids and gases) from an applied math perspective, starting with an introduction to the Navier-Stokes equations and other PDEs used to model fluids. The emphasis will be on physically relevant properties of solutions that can be deduced mathematically. The course will have more mathematics than a typical physics or engineering fluids course, including basic functional analysis and variational methods, and it will have more physics than a pure PDE analysis course. Through detailed study of several fundamental model systems, we will see PDE examples of topics that may be more familiar in the context of ODE dynamical systems, such as linear stability, nonlinear stability, bifurcations and chaos. Introductory-level knowledge of PDEs and real analysis will be assumed.
This course will be a PIMS network-wide graduate course, so it can be taken remotely for credit by students from any Canadian university in the PIMS network.