Stability of ideal plane flows

Ideal plane flows are incompressible inviscid two dimensional fluids, described mathematically by the Euler equations. Infinitely many steady states exist. The stability of these steady states is a very classical problem initiated by Rayleigh in 1880. It is also physically very important since instability is believed to cause the onset of turbulence of a fluid. Nevertheless, progress in its understanding has been very slow. I will discuss several concepts of stability and some linear stability and instability criteria. In some cases nonlinear stability and instability can be showed to follow from linear results. I will also briefly describe some ideas in the proof of these results.

Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).