Speaker: 

Isom Herron, Rensselaer Polytechnic Institute

Title: 

A new look at the principle of exchange of stabilities   

Abstract: 

In the classic work of Chandrasekhar, Hydrodynamic and Hydromagnetic
Stability, one of the most referenced ideas is this principle, which
is now described as "In the linearized stability problem, the first
unstable eigenvalue has imaginary part equal to zero". For some
problems, this situation is clear, when the underlying operator is
self-adjoint. For other problems, this principle has defied suitable
verification. We have developed techniques based on the analyzing the
resolvent structure such as, among other things, positive Green's
functions as oscillation kernels, which verifies this in diverse
contexts: Taylor-Couette flow, convection problems and others.