Abstract
The Vlasov equation may be used to model the dynamics of a collisionless plasma. We consider a situation where the plasma has unbounded support and the charge density does not decay as |x|→ ∞. The electric field is computed from the screened Poisson equation, whose fundamental solution decays exponentially as |x|→ ∞ and hence gives a convergent integral despite the lack of decay of the charge density. The limit as the screening is removed is studied in one space dimension. It is shown that if some assumptions on the initial conditions hold, then the limit in question exists (but is not uniform) and the problem satisfied by the limit is identified.
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Communicated by C. Mouhot
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Schaeffer, J. The Screened Poisson–Vlasov System with Infinite Charge and Vanishing Screening. Commun. Math. Phys. 333, 97–116 (2015). https://doi.org/10.1007/s00220-014-2198-3
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DOI: https://doi.org/10.1007/s00220-014-2198-3