Volumorphism geometry and fluid mechanics

Stephen Preston
CU Boulder, Mathematics

I will describe the Arnold program of viewing the equations of inviscid fluid mechanics as a geodesic equation on the space of volumorphisms. This approach leads to a geometric description of Lagrangian stability, along with nice existence and uniqueness results.

I will not assume any knowledge of Riemannian geometry; instead I will explain the geometry as it arises naturally in this approach. The talk will be essential preparation for the seminar of my colleague Gerard Misiolek, who is speaking on October 12 on the same topic. Questions and interruptions will be welcome