- Series
- PDE Seminar
- Time
- Tuesday, February 2, 2010 - 3:10pm for 1 hour (actually 50 minutes)
- Location
- Skiles 255
- Speaker
- Zhiwu Lin – Georgia Tech
- Organizer
- Zhiwu Lin

Couette flows are shear flows with a linear velocity profile.
Known by Orr in 1907, the vertical velocity of the linearized
Euler equations at Couette flows is known to decay in time, for
L^2 vorticity. It is interesting to know if the perturbed Euler
flow near Couette tends to a nearby shear flow. Such problems
of nonlinear inviscid damping also appear for other stable flows
and are important to understand the appearance of coherent
structures in 2D turbulence. With Chongchun Zeng, we constructed
non-parallel steady flows arbitrarily near Couette flows in
H^s (s<3/2) norm of vorticity. Therefore, the nonlinear inviscid
damping is not true in (vorticity) H^s (s<3/2) norm. We also
showed that in (vorticity) H^s (s>3/2) neighborhood of Couette
flows, the only steady structures (including travelling waves) are
stable shear flows. This suggests that the long time dynamics near
Couette flows in (vorticity) H^s (s>3/2) space might be simpler.
Similar results will also be discussed for the problem of
nonlinear Landau damping in 1D electrostatic plasmas.