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Growth estimates and uniform decay for a collisionless plasma

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  • We consider the classical Vlasov-Poisson system in three space dimensions in the electrostatic case. For smooth solutions starting from compactly supported initial data, an estimate on velocities is derived, showing an upper bound with a growth rate no larger than $(t\ln t)^{6/25}$. As a consequence, a decay estimate is obtained for the electric field in the $L^\infty$ norm.
    Mathematics Subject Classification: Primary: 82D10; Secondary: 35B40, 76X05.

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