Asymptotic growth of support and uniform decay of moments for the vlasov-poisson system

Abstract

We consider asymptotic behaviors of classical solutions and weak solutions to the three-dimensional Vlasov{Poisson system in the plasma physics case. For a smooth solution with compactly supported initial datum, its velocity support is shown to grow like (t + 1) 15 2 ln 15 8 (t + 2). For a weak solution with bounded initial velocity-spatial moments or spatial moments of order > 2, we establish some decay results for its high velocity-spatial moments.