Nonlinear Waves Trimester - May Conference

Collection Nonlinear Waves Trimester - May Conference

Organizer(s) Frank MERLE (Université de Cergy-Pontoise & IHÉS), Pierre RAPHAËL (Université Nice Sophia-Antipolis), Nikolay TZVETKOV (Université de Cergy-Pontoise)

Date(s) 23/05/2016 - 27/05/2016

linked URL https://indico.math.cnrs.fr/event/889/

00:00:00 / 00:00:00

12 21

Some Landau damping results for the HMF model and its discrete time approximation

We consider solutions of the Vlasov-HMF model starting in a small Sobolev neighborhood of a spatially homogeneous stationary state satisfying a linear stability criterion and prove a scattering result (Landau damping). We then consider time discretizations of these solutions based on splitting methods between the linear and non-linear part of the equation and we prove that the numerical solutions converge weakly to a modified state which is close to the continuous one. We also prove that our numerical scheme is uniformly convergent, with a convergence rate of order one for Lie splittings, and two for Strang splittings. We will also consider the case of non-homegeous states for which action-angle variables can be used

Information about the video

Date of recording 25/05/2016
Date of publication 03/06/2016
Institution IHES
Licence CC BY-NC-ND
Format MP4

Domain(s)

Numerical Analysis

MSC codes

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