相关论文: Scattering problem for Vlasov-type equations on th…
We consider the Vlasov-Poisson system with initial data a small, radial, absolutely continuous perturbation of a point charge. We show that the solution is global and disperses to infinity via a modified scattering along trajectories of the…
In view of applications to electron-positron pair-plasmas and fullerene pair-ion-plasmas containing charged dust impurities a thorough discussion is given of three-component Plasmas. Space-time responses of multi-component linearized Vlasov…
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in…
We study the quasineutral limit of a Vlasov-Poisson system that describes the dynamics of ions in a plasma. We handle data with Sobolev regularity under the sharp assumption that the profile of the initial data in the velocity variable…
We present perturbation theory based on the inverse scattering transform method for solitons described by an equation with the inverse linear dispersion law $\omega\sim 1/k$, where $\omega$ is the frequency and $k$ is the wave number, and…
One of the difficulties associated with the scattering problems arising in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider…
A general solution to linearized Vlasov equation for an electron electrostatic wave in a homogeneous unmagnetized plasma is derived. The quasi-linear diffusion coefficient resulting from this solution is a continuous function of omega in…
This paper concerns the linear Landau damping for the two species Vlasov-Poisson system for ions and electrons near Penrose stable equilibria. The result is an extension of the result on the one species Vlasov-Poisson equation by Mouhout…
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 consider the focusing nonlinear Schr\"odinger equation $i u_t + \Delta u + |u|^{p-1}u=0$, $p>1,$ and the generalized Hartree equation $iv_t + \Delta v + (|x|^{-(N-\gamma)}\ast |v|^p)|v|^{p-2}u=0$, $p\geq2$, $\gamma<N$, in the…
In this paper, we establish the stability of the quasineutral limit for the ionic Vlasov-Poisson system under perturbations exponentially small in Wasserstein sense. Notably, we emphasize that exponential smallness is a necessary condition…
We have developed a deterministic conservative solver for the inhomogeneous Fokker-Planck-Landau equation coupled with the Poisson equation, which is a {classical mean-field} primary model for collisional plasmas. Two subproblems, i.e. the…
We prove the existence and stability of flat steady states of the Vlasov-Poisson system, which in astrophysics are used as models of disk-like galaxies. We follow the variational approach developed by Guo and Rein for this type of problems…
Potential scattering problems governed by the time-dependent Gross-Pitaevskii equation are investigated numerically for various values of coupling constants. The initial condition is assumed to have the Gaussian-type envelope, which differs…
In this paper, we study the Vlasov-Poisson-Landau Equations on $\mathbb{T}^3\times \mathbb{R}^3$ with small collision frequency $\nu\ll 1$. We prove that for $\nu$-independent perturbations of the global Maxwellians in Gevrey-$2_-$,…
We extend our analysis of divergence-free positive symmetric tensors (DPT) begun in a previous paper. On the one hand, we refine the statements and give more direct proofs. Next, we study the most singular DPTs, and use them to prove that…
We prove that for any global solution to the Vlasov-Maxwell system arising from compactly supported data, and such that the electromagnetic field decays fast enough, the distribution function exhibits a modified scattering dynamic. In…
Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma, an exact relativistic hydrodynamic closure for a special type of water-bag distributions satisfying the Vlasov equation has…
We consider the Zakharov-Kuznetsov equation in space dimension 3: \[ \left\{ \begin{array}{l} \partial_t u + \partial_x \Delta u + \partial_x \frac{u^2}{2} = 0 \\ u(t = 0) = u_0 \end{array} \right. \] where $u : (t, x, y) \in \mathbb{R}…
The Novikov-Veselov (NV) equation is a dispersive (2+1)-dimensional nonlinear evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries (KdV) equation. This paper considers the stability of plane wave soliton solutions of…