相关论文: On the Existence of Exponentially Decreasing Solut…
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyaponuv function, we prove that when the damping is linear, we can find initial…
Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for…
We consider the repulsive Vlasov-Poisson system in dimension $d \geq 4$. A sufficient condition on the decay rate of the associated electric field is presented that guarantees the scattering and determination of the complete asymptotic…
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.
The evolution of an initial perturbation in Vlasov plasma is studied in the intrinsically nonlinear long-time limit dominated by the effects of particle trapping. After the possible transient linear exponential Landau damping, the evolution…
We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are small perturbations of homogeneous Penrose-stable equilibria. We also prove the…
For the Vlasov-Poisson equation with random uncertain initial data, we prove that the Landau damping solution given by the deterministic counterpart (Caglioti and Maffei, {\it J. Stat. Phys.}, 92:301-323, 1998) depends smoothly on the…
In this paper, we study the Vlasov-Poisson-Fokker-Planck (VPFP) equation with a small collision frequency $0 < \nu \ll 1$, exploring the interplay between the regularity and size of perturbations in the context of the asymptotic stability…
In these short, rather informal, expository notes I review the current state of the field regarding the mathematics of Landau damping, based on lectures given at the CIRM Research School on Kinetic Theory, November 14--18, 2022. These notes…
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…
We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be…
We study the linearized Vlasov equations and the linearized Vlasov-Fokker-Planck equations in the weakly collisional limit in a uniform magnetic field. In both cases, we consider periodic confinement and Maxwellian (or close to Maxwellian)…
We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov-Poisson systems with screened interactions in the whole space $\mathbb{R}^d$ (for $d\geq3$) that was first established by Bedrossian, Masmoudi and Mouhot.…
We considered classical solutions to the initial boundary value problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We obtained global a priori estimates and global existence results of classical…
It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for…
This short note provides explicit solutions to the linearized Boussinesq equations around the stably stratified Couette flow posed on $\mathbb{T}\times\mathbb{R}$. We consider the long-time behavior of such solutions and prove inviscid…
In this paper, we consider the linearized Vlasov-Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter $\eps$ in front of the collision operator which will tend to $0$. Moreover,…
We consider the Vlasov-Poisson equation in $\mathbb{R}^3$ with initial data which are not $L^1$ in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we…
We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…
Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…