Wednesday, April 15, 2009. Minnesota joint Dynamical Systems and PDE seminar

Speaker: Professor Thierry Gallay, Universite de Grenoble I.

Title:  Spectral and pseudospectral estimates for a semiclassical
        non-selfadjoint operator arising in fluid mechanics.

Abstract: Fluid mechanics provides a variety of examples of non-selfadjoint operators with interesting 
spectral and pseudospectral properties. One of these is the linearized operator at the Lamb-Oseen vortex, 
which is an explicit self-similar solution of the two-dimensional Navier-Stokes equation. 
Motivated by this problem, we consider in this talk a simple one-dimensional operator which is a large 
skew-symmetric perturbation of the harmonic oscillator. Using variational hypocoercive methods, 
and semiclassical subelliptic estimates, we obtain accurate spectral and pseudospectral estimates 
which explain qualitatively what is observed numerically in the original problem. 
This is a joint work with I. Gallagher (Paris 7) and F. Nier (Rennes).

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