Together with Cédric Villani, we have just posted a new version of our preprint “On Landau damping”:
Here are the main novelties in this version:
(1) The main result now covers Coulomb and Newton potentials (i.e. with global in time stability and damping). This is based on a new idea: echoes occurring at different frequencies are asymptotically well separated, which allows to improve on our “echoes estimates”.
(2) Our results now are also extended to some classes of Gevrey data (this was already allowed in the previous version for potentials less singular than Coulomb, whereas for Coulomb this is a consequence of the better echoes control mentionned above). This allows for compactly supported perturbations.
(3) As a corollary our work now includes new results of stability for homogeneous equilibria of the Vlasov–Poisson equation, including the stability of certain nonmonotone distributions in the repulsive case (a longstanding open problem), and stability below the Jeans length in the attractive case.
Any comment is welcome.