PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Victor Nistor, Stephanie Zerby, Mark Levi, Jinchao Xu, Ludmil Zikatanov.

Title:Nonlinear Landau damping
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Zhiwu Lin, Georgia Tech Mathematics
Abstract:
Consider electrostatic plasmas described by Vlasov-Poisson equation 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 under analytic perturbations by Mouhot and Villani, but for general perturbations the problem is still largely open. With Chongchun Zeng, we construct nontrivial traveling waves (BGK waves) with any spatial period which are arbitrarily near any homogeneous state in H^s (s<3/2) Sobolev norm of the distribution function. Therefore, the nonlinear Landau damping is not true in H^s (s<3/2) spaces. We also showed that in small H^s (s>3/2) neighborhoods of linearly stable homogeneous states, there exist no nontrivial invariant structures. Our results suggest that for subcritical perturbations (s<3/2) the nonlinear trapping effect cannnot be ignored even in the limit of small amplitude; for supercritical perturbations (s>3/2), such trapping effect might have no influence on the long time dynamics and the nonlinear damping is hopeful. Similar results were also obtained for the problem of nonlinear inviscid damping of Couette flow, for which the linear decay was first observed by Orr in 1907.

Room Reservation Information

Room Number:MB106
Date:04 / 12 / 2013
Time:03:35pm - 04:25pm