Related papers: Scattering problem for Vlasov-type equations on th…
In this paper, we study small data solutions to the Vlasov-Poisson system with the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flow. First, we provide a new proof of global existence for…
Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs arising in various problems of mathematical physics and intensively studied in the recent literature. This report is aiming to solve the…
The Novikov-Veselov (NV) equation is a (2+1)-dimensional nonlinear evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries (KdV) equation. Solution of the NV equation using the inverse scattering method has been discussed…
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions…
We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$. More precisely, we show that small, smooth, and localized perturbations of the Poisson…
We study the asymptotic behavior of small data solutions to the screened Vlasov-Poisson equation on $\mathbb{R}^d\times\mathbb{R}^d$ near vacuum. We show that for dimensions $d\geq 2$, under mild assumptions on localization (in terms of…
In this paper, we prove the decay and scattering in the energy space for nonlinear Schr\"odinger equations with regular potentials in $\Bbb R^d$ namely, $i{\partial _t}u + \Delta u - V(x)u + \lambda |u|^{p - 1}u = 0$. We will prove decay…
We study the long-time behavior of radially symmetric solutions to the Vlasov-Poisson equation consisting of an attractive point mass and a small, suitably localized and absolutely continuous distribution of particles: if the latter is…
In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave…
This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell system. The surface…
We study the expansion of ultracold neutral plasmas in the regime in which inelastic collisions are negligible. The plasma expands due to the thermal pressure of the electrons, and for an initial spherically symmetric Gaussian density…
We discuss a new family of solutions of the Grad--Shafranov (GS) equation that describe D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry…
We give a new, simpler, proof of nonlinear Landau damping on T^d in Gevrey-1/s regularity (s > 1/3) which matches the regularity requirement predicted by the formal analysis of Mouhot and Villani in the original proof of Landau damping…
In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the $ (2 + 1) $--dimensional analog of the KdV equation integrable by the method of inverse scattering for the two--dimensional…
We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by…
We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature $\kappa\ne 0$: the unit sphere $\mathbb S^2$, for $\kappa>0$, and the unit hyperbolic sphere $\mathbb H^2$, for…
A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for…
This review presents an upgraded wave theory adapted to the high fluctuation level of driven realistic i.e. non-idealized plasmas. Above all, this means giving up the well-known concept of a linear wave theory in favor of a thoroughly…
A hybrid model of the Vlasov equation in multiple spatial dimension $D>1$ [H. A. Rose and W. Daughton, Physics of Plasmas v. 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a…