Exact Large Time Behavior of Spherically Symmetric Plasmas
Exact Large Time Behavior of Spherically Symmetric Plasmas
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DOI：
10.1137/20m1352508
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发表时间：
2020-06
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影响因子：
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通讯作者：
S. Pankavich
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作者：
S. Pankavich
我们考虑了具有球对称初始数据的经典和相对论Vlasov-Poisson系统，并证明了在分布函数的支持下，对于所有合适的电荷密度和电场的$L^p$范数，最优衰减率以及最大粒子位置和动量的最优增长率.虽然以前的工作[霍斯特，E.，对称等离子体及其衰变。Comm.Math.Phys.1990，126：613-633]建立了电荷密度和电场上确界衰减的上界，我们提供了一个稍微不同的证明，获得了最优速率，并将该结果扩展到包括所有其他范数。此外，我们证明了上述每个量的尖锐下界，并建立了所有空间和动量特性的时间渐近行为。最后，我们调查的粒子分布和它的空间平均为$t \\infty$的限制行为。特别是，我们表明，前者弱收敛到零，而后者一致收敛到一个光滑的，紧支撑的功能，保持系统的质量，角动量和能量，只取决于限制粒子动量。
We consider the classical and relativistic Vlasov-Poisson systems with spherically-symmetric initial data and prove the optimal decay rates for all suitable $L^p$ norms of the charge density and electric field, as well as, the optimal growth rates for the largest particle position and momentum on the support of the distribution function. Though a previous work [Horst, E., Symmetric plasmas and their decay. Comm. Math. Phys. 1990, 126: 613-633] established upper bounds on the decay of the supremum of the charge density and electric field, we provide a slightly different proof, attain optimal rates, and extend this result to include all other norms. Additionally, we prove sharp lower bounds on each of the aforementioned quantities and establish the time-asymptotic behavior of all spatial and momentum characteristics. Finally, we investigate the limiting behavior of the particle distribution and its spatial average as $t \to \infty$. In particular, we show that the former converges weakly to zero, while the latter converges uniformly to a smooth, compactly-supported function that preserves the mass, angular momentum, and energy of the system and depends only upon limiting particle momenta.