Sydney Dynamics Group Seminar: Robert Marangell, University of Sydney -- Sydney Dynamics group Seminar

Seminar : Sydney Dynamics group Seminar 
Day/time : Thursday, May 14 at 4:00 PM,
Location: SMRI seminar room (A12 Macleay Room 301) 
Speaker : Robert Marangell, University of Sydney 

Title: An Evans function for the linearised 2D Euler equations using Hill's
determinant.  

Abstract: This talk concerns the point spectrum of the linearisation of Euler’s
equation for an ideal fluid on the torus, about a so-called shear flow.  By separation
of variables, the problem reduces to the spectral theory of a complex Hill equation.
Using Hill’s determinant, we construct an Evans function for the original linearised
Euler equation.  This Evans function gives a complete characterisation of the point
spectrum of the linearised operator and allows one to count the isolated eigenvalues
with non-zero real part.  For a particular shear flow, I will show that the number of
discrete eigenvalues of the linearised operator is exactly twice the number of non-zero
integer lattice points inside the so-called unstable disc.  This is joint work with
Holger Dullin, Yuri Latushkin, Shibi Vasudevan, and Joachim Worthington.