Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Inviscid damping and the asymptotic stability of planar shear flows

Jacob Bedrossian

New York University

We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D Euler equations of ideal, incompressible flow (joint with N. Masmoudi). That is, perturbations in a suitable norm (Gevrey 2-) converge back to a shear flow as t -> +/-infinity. The driving mechanism behind the stability is known as inviscid damping due to its close relationship with Landau damping in the Vlasov equations. Very recent work on Landau damping (joint with N. Masmoudi and C. Mouhot) will also be discussed if time permits.