论文标题
球形对称等离子体的确切时间行为
Exact Large Time Behavior of Spherically-Symmetric Plasmas
论文作者
论文摘要
我们考虑具有球形对称初始数据的经典和相对论的Vlasov-Poisson系统，并证明了电荷密度和电场的所有合适的$ l^p $规范的最佳衰减速率，以及最大的粒子位置和动量对分布功能的最大粒子位置和动量的最佳生长速率。尽管以前的工作\ cite {horst}在电荷密度和电场的衰减上建立了上限，但我们提供了略有不同的证明，达到最佳速度，并将此结果扩展到包括所有其他规范。此外，我们证明了上述量的每个空间和动量特征的时间 - 反应性行为。最后，我们研究了粒子分布的空间平均值的限制行为为$ t \ to \ infty $。特别是，我们表明它均匀收敛到平滑，紧凑的函数，该功能保留了系统的质量，角动量和能量，并且仅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 \cite{Horst} 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 spatial average of the particle distribution as $t \to \infty$. In particular, we show that it 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.
