Estimate of largest velocities for Vlasov–Poisson plasma with radiation damping

Abstract

In this article, we study the asymptotic behavior of classical solutions to three‐dimensional Vlasov–Poisson system with radiation damping arising in plasma physics. For smooth solutions with compact support in phase space, the growth estimate of the largest velocity of plasma particles is improved to Ofalse(false(t+1false)2false/15ln8false/15false(t+2false)false)$$ O\left({\left(t+1\right)}^{2/15}{\ln}^{8/15}\left(t+2\right)\right) $$. As a consequence, some better estimates of the charge density and electrostatic field are obtained.