Variational formulations of Euler Equations

Subscription
Subscription to the mailing list is also possible by sending an email with subject "subscribe" and empty email body to lecture-zizza-w25-join@mis.mpg.de

---

Next lectures
12.12.2025, 15:00 (E2 10 (Leon-Lichtenstein))
19.12.2025, 15:00 (E2 10 (Leon-Lichtenstein))
26.12.2025, 15:00 (E2 10 (Leon-Lichtenstein))
02.01.2026, 15:00 (E2 10 (Leon-Lichtenstein))
09.01.2026, 15:00 (E2 10 (Leon-Lichtenstein))
16.01.2026, 15:00 (E2 10 (Leon-Lichtenstein))
23.01.2026, 15:00 (E2 10 (Leon-Lichtenstein))

---

In 1966 Arnold interpreted Euler Equations as a geodesic Equation on the group of volume-preserving diffeomorphisms SDiff (or fluid configurations). Solutions of Euler Equations arise as critical points of the actional functional (i.e. kinetic energy). Unfortunately, the group SDiff is an object that is not much well understood. In dimension $d\geq 3$ it is possible to find $f\in SDiff$ for which a shortest path in SDiff does not exist, and in dimension $d=2$ there exists fluid configurations $f\in SDiff$ that are not attainable. To minimize the action functional, Brenier considered the class of Generalized Incompressible Flows: fluid particles do not follow a specified trajectory, but they can split in a continuum of trajectories. Still, it is not clear how to match the notion of Generalized Flows with the one of weak solutions of Euler.

Keywords
Group of volume-preserving diffeomorphisms, Euler Equations, Generalized Flows

Prerequisites
some differential geometry may help, but it is not needed