Nonlinear inviscid damping in 2D Euler

Jacob Bedrossian, CIMS

Abstract:
We prove the global asymptotic stability of shear flows close to planar Couette flow in the 2D incompressible Euler equations. Specifically, given
an initial perturbation of the Couette flow which is small in a suitable sense, we show that the velocity converges strongly in L2 to another shear
flow which is not far from Couette. This strong convergence is usually referred to as "inviscid damping" and is roughly analogous to Landau
damping in the Vlasov equations. Joint work with Nader Masmoudi.