PDE tasting - An invitation to some current problems in mathematical fluid mechanics

This intensive mini-course is aimed at undergraduate students of mathematics with a solid foundation of analysis and measure theory (background in PDE is not essential). The goal is to give a tasting of some of the great problems in mathematical fluid mechanics, from the perspective of the analysis of partial differential equations, focusing on the most basic models: the incompressible Euler and Navier-Stokes equations.

• Why is Jupiter's great red spot so stable that it has been observed for over 100 years, and how to explain the emergence of such coherent structures? Is this an example of self-organized dynamics?
• The butterfly effect of Lorenz in the case of chaotic finite-dimensional dynamical systems is well known. But Lorenz also predicted a much more catastrophic lack of determinism, the "real" butterfly effect: no matter how precise our measurements, we cannot predict the future of dynamical systems with "many" degrees of freedom.
• It was observed by Mandelbrot that turbulent flows exhibit fractal-like structures. Can such structures really arise as solutions of a PDE and how to interpret this?
• One of the 7 millenium prize problems is the question of singularity formation for the incompressible Navier-Stokes equations, or, simply stated: can water spontaneously explode? There are many other PDEs where singularity formation is interesting, so what makes the 3D Navier-Stokes equations so special (and the question so hard) that one puts a one-million dollar bounty on it?

The organizers of the School will take care of the accommodation of all the participants in Leipzig, of the morning and afternoon tea/coffee breaks as well as lunches during the days of the School.

The registration is closed.