Related papers: Landau damping and survival threshold
We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field) equation based on splitting methods between the linear and non-linear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially…
We carry out a systematic study of the dispersion relation for linear electrostatic waves in an arbitrarily degenerate quantum electron plasma. We solve for the complex frequency spectrum for arbitrary values of wavenumber $k$ and level of…
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near…
The propagation of an electrostatic wave packet inside a collisionless and initially Maxwellian plasma is always dissipative because of the irreversible acceleration of the electrons by the wave. Then, in the linear regime, the wave packet…
Vlasov-Poisson-Fokker-Planck (VPFP) simulations of large-amplitude electron plasma waves, where the bounce frequency is much larger than the collision frequency, $\omega_B \gg \nu_\text{ee}$, show that the evolution of these waves exhibits…
In this paper, we study the backward problem for the one-dimensional Vlasov-Poisson system with massless electrons, and we show the Landau damping by fixing the asymptotic behaviour of our solution.
We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small gas, i.e.\ measures of the form $\delta_{(\mathcal{X}(t),\mathcal{V}(t))}+\mu^2d{\bf x}d{\bf v}$ for some $(\mathcal{X},…
We provide few remarks on nonlinear Landau damping that concerns decay of the electric field in the classical Vlasov-Poisson system near spatially homogenous equilibria. In particular, this includes the analyticity framework, \`a la…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…
This research was stimulated by the recent studies of damping solutions in dynamically stable spherical stellar systems. Using the simplest model of the homogeneous stellar medium, we discuss nontrivial features of stellar systems. Taking…
Evolution of a Langmuir wave is studied numerically for finite amplitudes slightly above the threshold which separates damping from nondamping cases. Arrest of linear damping is found to be a second-order effect due to ballistic evolution…
Using the Vlasov-wave formalism, it is shown that self-consistency vanishes in the plateau regime of the bump-on-tail instability if the plateau is broad enough. This shows that, in contrast with the "turbulent trapping" Ansatz, a…
The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a…
We revisit the effect of non-linear Landau (NL) damping on the electrostatic instability of blazar-induced pair beams, using a realistic pair-beam distribution. We employ a simplified 2D model in ${\bf k}$-space to study the evolution of…
We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac-Heisenberg-Wigner formalism. The vacuum contribution to the physical observables leads to ultra-violet divergences, that…
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu…
We consider the spatially inhomogeneous Landau equation with soft potentials, including the case of Coulomb interactions. First, we establish the existence of solutions for a short time, assuming the initial data is in a fourth-order…
We study the nonlinear propagation of ion-acoustic waves (IAWs) in an unmagnetized collisionless plasma with the effects of electron and ion Landau damping in the weak quantum (semiclassical) regime, i.e., when the typical ion-acoustic (IA)…
This work deals with the Landau equation in a bounded domain with the Maxwell reflection condition on the boundary for any (possibly smoothly position dependent) accommodation coefficient and for the full range of interaction potentials,…
We consider the wave equation with Kelvin-Voigt damping in a bounded domain. The exponential stability result proposed by Liu and Rao or T\'ebou for that system assumes that the damping is localized in a neighborhood of the whole or a part…