Mathematical Hydrodynamics

Hydrodynamics is as old and many-faceted subject that has motivated the development of several areas of mathematics, including partial differential equations, harmonic analysis, dynamical systems and statistical mechanics. In this lecture course the aim is to give an introduction to several aspects of this vast subject, mostly focussing on incompressible models (Euler and Navier-Stokes equations).
Topics to be discussed are

• Hydrodynamic stability and instability
• Turbulence
• Theory of weak solutions

References

• D. Acheson Elementary Fluid Dynamics
• A. Majda and A. Bertozzi Vorticity and incompressible flow
• C. Marchioro and M. Pulvirenti Mathematical Theory of Incompressible Nonviscous Fluids
• U. Frisch Turbulence

Date and time info
Tuesday and Wednesday 11:15 - 12:45

Keywords
partial differential equations, harmonic analysis, dynamical systems, statistical mechanics

Prerequisites
Solid background in functional analysis and knowledge of partial differential equations (FA1, PDG1). Knowledge of continuum mechanics and some theoretical physics is useful but not required.

Audience
MSc students, PhD students, Postdocs

Language
English