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Antoine Gagnebin

Publications and source records attributed to Antoine Gagnebin.

5 recordsLinked to original sources
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

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↗
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↗