On the 3-D Vlasov–Poisson system with point charges: Global solutions with unbounded supports and propagation of velocity-spatial moments

Asymptotic growth bounds for the 3‐D Vlasov‐Poisson system with point charges

“…Recently, global existence and uniqueness of classical solutions without assumption of finite kinetic energy but with compact "velocity-spatial support" for the Vlasov-Poisson system (5)-(6) were established in reference Chen and Zhang. 20 These results were successfully extended to the plasma-charge model (1)-(4) with = 1 in Li and Zhang, 23 where the authors obtained an exponential type estimate about the velocity-spatial supports of solutions with infinite kinetic energy, namely,…”

“…Next, we recall an essential tool introduced in Li and Zhang, 23 namely, the pointwise energy of a plasma particle relative to the th point charge:…”

Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

“…The presence of a point charge introduces singular electric fields and significantly complicates the analysis. Nevertheless, global existence and uniqueness of strong solutions when the support of the density is separated from the point charge has been established in [27], see also [5] and references therein, while global existence of weak solutions for more general support was proved in [10] with subsequent improvements in [23,24,28]. We also refer to [9] where "Lagrangian solutions" are studied and to [6,7] for works in the case of attractive interactions.…”

“…Nevertheless, when the gas-point charge interaction is repulsive, global existence and uniqueness of strong solutions when the support of the density is separated from the point charge has been established in [36], see also [7] and references therein. Global existence of weak solutions for more general support was then proved in [12] with subsequent improvements in [31,32,40], and a construction of "Lagrangian solutions" in [11]. For attractive interactions, strong well-posedness remains open, even locally in time, but global weak solutions have been constructed [8,9].…”

Stability of a point charge for the Vlasov-Poisson system: the radial case

“…The presence of a point charge introduces singular electric fields and significantly complicates the analysis. Nevertheless, global existence and uniqueness of strong solutions when the support of the density is separated from the point charge has been established in [24], see also [4] and references therein, while global existence of weak solutions for more general support was proved in [9] with subsequent improvements in [20,21,25]. We also refer to [8] where "Lagrangian solutions" are studied and to [5,6] for works in the case of attractive interactions.…”