Sub-linear estimate of large velocities in a collisionless plasma

Abstract

We consider the Vlasov-Poisson system in three space dimensions in the electrostatic case. For a smooth solution with compactly supported initial datum, the growth estimate of its velocity support is improved to t-2/11+εfor any +ε0. As a consequence, we obtain a better decay estimate of the electrical field, namely ||E||∞=O(t-1/11+ε) as t→α. © 2014 International Press.