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Focusing Solutions of the Vlasov-Poisson System
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math.APmath-phmath.MP
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solutionssystemvlasov-poissonarbitrarilynormsattaincasecharge
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We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initially possess arbitrarily small C^k norms for the charge densities and the electric fields, but attain arbitrarily large L^1 norms of them at some later time.
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