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Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations
In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove theExpand
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Stability Issues in the Quasineutral Limit of the One-Dimensional Vlasov–Poisson Equation
This work is concerned with the quasineutral limit of the one-dimensional Vlasov–Poisson equation, for initial data close to stationary homogeneous profiles. Our objective is threefold: first, weExpand
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On the controllability of the relativistic Vlasov–Maxwell system
In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometricExpand
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The three-dimensional finite Larmor radius approximation
  • Daniel Han-Kwan
  • Mathematics, Computer Science
  • Asymptot. Anal.
  • 13 December 2008
TLDR
We rigorously establish the asymptotic gyrokinetic limit of the rescaled and modified Vlasov-Poisson system in a three-dimensional setting with the help of an averaging lemma. Expand
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Quasineutral Limit of the Vlasov-Poisson System with Massless Electrons
In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behavior of ions in a plasma. We considerExpand
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Effect of the polarization drift in a strongly magnetized plasma
We consider a strongly magnetized plasma described by a Vlasov-Poisson system with a large external magnetic field. The finite Larmor radius scaling allows to describe its behaviour at very fineExpand
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Quasineutral limit for Vlasov-Poisson via Wasserstein stability estimates in higher dimension
This work is concerned with the quasineutral limit of the Vlasov-Poisson system in two and three dimensions. We justify the formal limit for very small but rough perturbations of analytic initialExpand
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The quasineutral limit of the Vlasov-Poisson equation in Wasserstein metric
In this work, we study the quasineutral limit of the one-dimensional Vlasov-Poisson equation for ions with massless thermalized electrons. We prove new weak-strong stability estimates in theExpand
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Geometric Analysis of the Linear Boltzmann Equation I. Trend to Equilibrium
This work is devoted to the analysis of the linear Boltzmann equation on the torus, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in theExpand
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Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimates
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 firstExpand
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