Searcharxiv⌕ Search

arXiv subjects

Mikaela Iacobelli

Publications and source records attributed to Mikaela Iacobelli.

At least 19 recordsLinked to original sources
arXiv2026

Stability in Quasineutral Plasmas with Thermalized Electrons

We study the quasineutral limit for the ionic Vlasov-Poisson system with thermalized electrons (VPME) on the torus in dimensions one to three, for rough solutions with bounded spatial density. Our main result is a quantitative stability theorem showing that quasineutral convergence is robust under exponentially small perturbations of the initial data, as measured in Wasserstein distance: given a regular family of reference solutions for which the quasineutral limit is known to hold, we prove that the same limit remains valid for perturbed solutions on the same time interval. The proof combines a kinetic-Wasserstein stability framework with a refined analysis of the Poisson-Boltzmann coupling specific to VPME. A central new ingredient is an improved control of the characteristic flow: we obtain quantitative bounds on the growth of characteristics in the velocity coordinate, with only polynomial deterioration in the Debye length. This yields new locally-uniform-in-time bounds on the spatial density and provides the key input needed to complete the stability estimates. These results bring the stability theory for the ionic model in the quasineutral regime close to the known instability threshold and substantially relax the smallness conditions required in earlier works. As a byproduct, our approach improves the moment assumptions in the global well-posedness theory for bounded-density solutions to VPME on the torus.

math.AP↗
arXiv2026

Quantization of measures in Carnot groups

We study optimal quantization of probability measures on Carnot groups equipped with a left-invariant homogeneous distance. We prove two main results. First, we establish a Zador-type asymptotic formula for the quantization error: after the natural rescaling, the error converges as the number of centers tends to infinity, and the exponent is determined by the homogeneous dimension of the group. The limiting constant is a Carnot cell constant, defined through the quantization problem on a reference cell. Second, we prove weak convergence of the empirical measures associated with optimal centers, and describe the limit in terms of the density of the absolutely continuous part of the measure. The proof combines a tiling of Carnot groups by exponential cubes with a sub-Riemannian version of Pierce's lemma, which allows us to treat measures with non-compact support.

math.MG↗
arXiv2026

Quasineutral Plasmas and the Geometry of Kinetic Stability

This article presents an overview of quasineutral limits in plasma models. Starting from the Vlasov-Poisson system, it explains the role of the Debye length, the emergence of a kinetic incompressibility constraint, and the stability issues caused by fast oscillations and singular electric fields. A central theme is that the geometry of the kinetic flow should be reflected in the way perturbations are measured. This leads to kinetic Wasserstein distances adapted to phase-space dynamics, which provide refined stability estimates for quasineutral limits. The article also discusses related models with thermalized electrons and the additional challenges of the electromagnetic Vlasov-Maxwell setting.

math.AP↗
arXiv2026

On the stability of vacuum in the screened Vlasov-Poisson equation

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 spatial moments) and regularity (in terms of at most three Sobolev derivatives) solutions scatter freely. In dimension $d=1$, we obtain a long time existence result in analytic regularity.

math.AP↗
arXiv2025

Propagation of Velocity Moments for the Magnetized Vlasov-Poisson System with Space-Time Dependent Magnetic Fields

We prove that polynomial velocity moments of solutions to the 2D magnetized Vlasov-Poisson system and the 3D magnetized screened Vlasov-Poisson equation remain finite for all times, provided they are finite initially, even when the external magnetic field $B=B(t,x)$ is space-time dependent. We deduce propagation of regularity, thereby implying the existence of global classical solutions. Moreover, we prove optimal stability estimates in the kinetic-Wasserstein distance on par with the unmagnetised case.

math.AP↗
arXiv2025

Exponential convergence for ultrafast diffusion equations with log-concave weights

We study the asymptotic behavior of a weighted ultrafast diffusion PDE on the real line, with a log-concave and log-lipschitz weight, and prove exponential convergence to equilibrium. This result goes beyond the compact setting studied in [22]. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in [11].

math.AP↗
arXiv2025

Asymptotic quantization on Riemannian manifolds via covering growth estimates

The quantization problem looks for best approximations of a probability measure on a given metric space by finitely many points, where the approximation error is measured with respect to the Wasserstein distance. On particular smooth domains, such as $\mathbb{R}^d$ or complete Riemannian manifolds, the quantization error is known to decay polynomially as the number of points is taken to infinity, provided the measure satisfies an integral condition which controls the amount of mass outside compact sets. On Riemannian manifolds, the existing integral condition involves a quantity measuring the growth of the exponential map, for which the only available estimates are in terms of lower bounds on sectional curvature. In this paper, we provide a more general integral condition for the asymptotics of the quantization error on Riemannian manifolds, given in terms of the growth of the covering numbers of spheres, which is purely metric in nature and concerns only the large-scale growth of the manifold. We further estimate the covering growth of manifolds in two particular cases, namely lower bounds on the Ricci curvature and geometric group actions by a discrete group of isometries. These estimates can themselves generalize beyond manifolds, and hint at a future treatment of asymptotic quantization also on non-smooth metric measure spaces.

math.MG↗
arXiv2025

From relativistic Vlasov-Maxwell to electron-MHD in the quasineutral regime

We study the quasineutral limit for the relativistic Vlasov-Maxwell system in the framework of analytic regularity. Following the high regularity approach introduced by Grenier [44] for the Vlasov-Poisson system, we construct local-in-time solutions with analytic bounds uniform in the quasineutrality parameter $\varepsilon$. In contrast to the electrostatic case, the presence of a magnetic field and a solenoidal electric component leads to new oscillatory effects that require a refined decomposition of the electromagnetic fields and the introduction of dispersive correctors. We show that, after appropriate filtering, solutions converge strongly as $\varepsilon$ tends to zero to a limiting system describing kinetic electron magnetohydrodynamics (e-MHD). This is the first strong convergence result for the Vlasov-Maxwell system in the quasineutral limit under analytic regularity assumptions, providing a rigorous justification for the e-MHD reduction, widely used in modelling plasmas in tokamaks and stellarators.

math.AP↗
arXiv2024

Scattering problem for Vlasov-type equations on the $d$-dimensional torus with Gevrey data

In this article, we consider Vlasov-type equations describing the evolution of single-species type plasmas, such as those composed of electrons (Vlasov-Poisson) or ions (screened Vlasov-Poisson/Vlasov-Poisson with massless electrons). We solve the final data problem on the torus $\mathbb{T}^d$, $d \geq 1$, by considering asymptotic states of regularity Gevrey-$\frac{1}γ$ with $γ>\frac13$, small perturbations of homogeneous equilibria satisfying the Penrose stability condition. This extends to the Gevrey perturbative case, and to higher dimension, the scattering result in analytic regularity obtained by E. Caglioti and C. Maffei in [14], and answers an open question raised by J. Bedrossian in arXiv:2211.13707.

math.AP↗
arXiv2024

Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances

We extend Loeper's $L^2$-estimate relating the electric fields to the densities for the Vlasov-Poisson system to $L^p$, with $1 < p < +\infty$, based on the Helmholtz-Weyl decomposition. This allows us to generalize both the classical Loeper's $2$-Wasserstein stability estimate and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance to kinetic Wasserstein distances of order $1 < p < +\infty$.

math.AP↗
arXiv2024

Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov-Poisson

In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul's method from [Arch. Ration. Mech. Anal. 223:57-94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J. Stat. Phys. 177:20-60, 2019], with a new approach developed by the first author in [Arch. Ration. Mech. Anal. 244:27-50, 2022] to quantitatively improve stability estimates in kinetic theory.

math.AP↗
arXiv2023

Landau damping on the torus for the Vlasov-Poisson system with massless electrons

This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$ for the Vlasov-Poisson system with massless electrons (VPME). We consider solutions with analytic or Gevrey ($γ> 1/3$) initial data, close to a homogeneous equilibrium satisfying a Penrose stability condition. We show that for such solutions, the corresponding density and force field decay exponentially fast as time goes to infinity. This work extends the results for Vlasov-Poisson on the torus to the case of ions and, more generally, to arbitrary analytic nonlinear couplings.

math.AP↗
arXiv2023

On the local uniqueness of steady states for the Vlasov-Poisson system

Motivated by recent results of Lemou-Méhats-Räphael and Lemou concerning the quatitative stability of some suitable steady states for the Vlasov-Poisson system, we investigate the local uniqueness of steady states near these one. This research is inspired by analogous results of Couffrut and Šverák in the context of the 2D Euler equations.

math.AP↗
arXiv2021

Global well-posedness of Vlasov-Poisson-type systems in bounded domains

In this paper we prove global existence of classical solutions to the Vlasov-Poisson and the ionic Vlasov-Poisson models in bounded domains. On the boundary, we consider the specular reflection boundary condition for the Vlasov equation and either homogeneous Dirichlet or Neumann conditions for the Poisson equations.

math.AP↗
arXiv2021

A new perspective on Wasserstein distances for kinetic problems

We introduce a new class of Wasserstein-type distances specifically designed to tackle questions concerning stability and convergence to equilibria for kinetic equations. Thanks to these new distances, we improve some classical estimates by Loeper and Dobrushin on Vlasov-type equations, and we present an application to quasineutral limits.

math.AP↗
arXiv2021

Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an exponential nonlinearity that creates several mathematical difficulties. In particular, while global well-posedness in 3D is well understood in the electron case, this problem remained completely open for the ion model with massless electrons. The aim of this paper is to fill this gap by proving uniqueness for VPME in the class of solutions with bounded density, and global existence of solutions with bounded density for a general class of initial data, generalising all the previous results known for VP.

math.AP↗
arXiv2021

Global strong solutions in $\mathbb{R}^3$ for ionic Vlasov-Poisson systems

Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this article, we prove global well-posedness for two Vlasov-Poisson systems for ions, posed on the whole three-dimensional Euclidean space $\mathbb{R}^3$, under minimal assumptions on the initial data and the confining potential.

math.AP↗