Nonlinear Landau damping and inviscid damping

Thursday, June 30, 2011 - 12:00pm - 12:30pm
Lind 305
Zhiwu Lin (Georgia Institute of Technology)
Consider electrostatic plasmas described by 1D Vlasov-Poisson with a fixed ion background. In 1946, Landau discovered the linear decay of electric field near a stable homogeneous state. The nonlinear Landau damping was recently proved for analytic perturbations by Villani and Mouhot, but for general perturbations the problem is still largely open.
With Chongchun Zeng at Georgia Tech, we construct nontrivial traveling waves (BGK waves) with any spatial period which are arbitrarily near any homogeneous state in H^s (s3/2) neighborhoods of linearly stable homogeneous states, there exist no nontrivial invariant structures. This suggests that the long time dynamics near
stable homogeneous states in H^s (s>3/2) spaces might be much simpler and the nonlinear damping might be hopeful. We also obtained similar results for the problem of nonlinear inviscid damping of Couette flow, for which the linear decay was first observed by Orr in 1907.
MSC Code: