Fluid Mechanics

As the Euler theory of hydrodynamics (1757), the Born-Infeld theory of electromagnetism (1934) enjoys a simple and beautiful geometric structure. Quite surprisingly, the BI model which is of relativistic nature, shares many features with classical hydro- and magnetohydro-dynamics. In particular, I will discuss its very close connection with Moffatt’s topological approach to Euler equations, through the concept of magnetic relaxation.

The Marsden Memorial Lecture Series is dedicated to the memory of Jerrold E Marsden (1942-2010), a world-renowned Canadian applied mathematician. Marsden was the Carl F Braun Professor of Control and Dynamical Systems at Caltech, and prior to that he was at the University of California (Berkeley) for many years. He did extensive research in the areas of geometric mechanics, dynamical systems and control theory. He was one of the original founders in the early 1970’s of reduction theory for mechanical systems with symmetry, which remains an active and much studied area of research today.

This lecture is part of the Centre Interfacultaire Bernoulli Workshop on Classic and Stochastic Geometric Mechanics, June 8-12, 2015, which in turn is a part of the CIB program on

Geometric Mechanics, Variational and Stochastic Methods, 1 January to 30 June 2015.

I will present a survey of modelling, computational, and analytical work on thin liquid films of viscous fluids. I will particularly focus on films that are being acted on by more than one force. For example, if you've painted the ceiling, how do you model the effects of surface tension and gravity? How do you study the dynamics of the air/liquid interface? How do things change if you're considering a freshly painted wall? Or floor?