Moment Propagation of the Vlasov-Poisson System with a Radiation Term

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

“…Well‐posedness and asymptotic behavior for the system () has been well understood(see previous studies 2–5 ). Specifically, for $$$ {f}_0^{\pm}\in {C}_c^{\infty}\left({\mathbb{R}}^6\right) $$$, Kunze and Rendall proved the global existence and uniqueness of classical solutions and obtained the large time asymptotic behavior of the charge density $$$ \rho \left(t,x\right) $$$, the electrostatic field $$$ E\left(t,x\right) $$$ and the damping term $$$ {D}^{\left[2\right]}(t) $$$ 2 .…”

“…Well-posedness and asymptotic behavior for the system (1.1) has been well understood(see previous studies [2][3][4][5] ). Specifically, for 𝑓 ± 0 ∈ C ∞ c (R 6 ), Kunze and Rendall proved the global existence and uniqueness of classical solutions and obtained the large time asymptotic behavior of the charge density 𝜌(t, x), the electrostatic field E(t, x) and the damping term D [2] (t).…”

“…When $$$ {f}_0^{\pm}\in {C}_0^1\bigcap {L}^1\left({\mathbb{R}}^6\right) $$$ with bounded velocity‐spatial support, Xiao and Zhang 4 proved global existence and uniqueness of a classical solution with possibly infinite energy. And the propagation for velocity and velocity‐spatial moments of order greater than 2 has been studied in Xiao and Zhang 5 …”

“…And the propagation for velocity and velocity-spatial moments of order greater than 2 has been studied in Xiao and Zhang. 5 If we ignore the radiation damping and consider a monopolar particle system, that is, setting 𝜎 = 0 and 𝑓 − = 0, then system (1.1) degenerates to the classical Vlasov-Poisson system, which has been widely studied and well understood (see, e.g., previous studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein). Specifically, the asymptotic behavior in terms of estimating its largest velocity has received a great deal of attention in the past decades.…”