Nonlinear stability and instability of relativistic Vlasov‐Maxwell systems
Nonlinear stability and instability of relativistic Vlasov‐Maxwell systems
复制标题
相对论性 Vlasov-Maxwell 系统的非线性稳定性和不稳定性
DOI：
10.1002/cpa.20161
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发表时间：
2007
影响因子：
3
通讯作者：
W. Strauss
中科院分区：
文献类型：
--
作者：
Zhiwu Lin;W. Strauss
证明了1/2维相对论Vlasov-Maxwell系统某些周期平衡点的非线性稳定性或不稳定性。特别地，对于电场为零的纯磁平衡，我们用几种新的方法推广了通常的Casimir能量方法，证明了它在一个严格的判据下的非线性稳定性。对于一般的电磁平衡，我们证明了非线性不稳定是由线性不稳定引起的。非线性不稳定性是宏观的，只涉及电磁场的L1范数。©2006威利期刊公司。
We prove the nonlinear stability or instability of certain periodic equilibria of the 1½D relativistic Vlasov‐Maxwell system. In particular, for a purely magnetic equilibrium with vanishing electric field, we prove its nonlinear stability under a sharp criterion by extending the usual Casimir‐energy method in several new ways. For a general electromagnetic equilibrium we prove that nonlinear instability follows from linear instability. The nonlinear instability is macroscopic, involving only the L1‐norms of the electromagnetic fields. © 2006 Wiley Periodicals, Inc.