On linear Landau Damping for relativistic plasmas via Gevrey regularity

Relativistic Landau damping of longitudinal waves in isotropic pair plasmas

Propagation of Gevrey Regularity for Solutions of Landau Equations

There are many papers concerning the propagation of regularity for the solution of the Boltzmann equation (cf. [5, 6, 8, 9, 13] and references therein). In these works, it has been shown that the Sobolev or Lebesgue regularity satisfied by the initial datum is propagated along the time variable. The solutions having the Gevrey regularity for a finite time have been constructed in [15] in which ...

Nonlinear echoes and Landau damping with insufficient regularity

We prove that the theorem of Mouhot and Villani on Landau damping near equilibrium for the Vlasov-Poisson equations on Tx × Rv cannot, in general, be extended to Sobolev spaces. This is demonstrated by constructing a sequence of homogeneous background distributions and arbitrarily small perturbations in Hs which deviate arbitrarily far from free transport for long times (in a sense to be made p...

Gevrey Regularity for the Solution of the Spatially Homogeneous Landau Equation

This is a non-linear diffusion equation, and the coefficients āi j, c̄ depend on the solution f . Here we are mainly concerned with the Gevrey class regularity for the solution of the Landau equation. This equation is obtained as a limit of the Boltzmann equation when the collisions become grazing (see [8] and references therein). Recently, a lot of progress has been made on the study of the Sob...

On Landau Damping

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families...