Landau damping in relativistic plasmas
Landau damping in relativistic plasmas
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相对论等离子体中的朗道阻尼
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发表时间：
2014
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通讯作者：
Brent Young
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作者：
Brent Young
我们通过研究环面上的相对论弗拉索夫-泊松 (rVP) 系统来研究相对论等离子体中的朗道阻尼现象，以获得足够接近空间均匀稳态的初始数据。我们发现，如果稳态足够规则（本质上是在指定范围内的 Gevrey 度类），并且如果初始数据与该稳态的偏差在一定范数内足够小，则系统的演化使得其空间密度准指数地快速接近均匀常数值（即，像对于 ν ́ ε (0,1) 的 exp(−Ct ν ́) ）。我们先验假设这样的初始数据推出的解在所有时间都存在（决不能用 rVP 保证，但这是一个合理的假设，因为我们接近空间均匀状态），并且所讨论的各种范数在时间上是连续的（这应该是柯西-科瓦列夫斯卡亚定理的抽象版本的结果）。此外，我们必须假设一种“逆庞加莱不等式”...
We examine the phenomenon of Landau damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson (rVP) system on the torus for initial data sufficiently close to a spatially uniform steady state. We find that if the steady state is regular enough (essentially in a Gevrey class of degree in a specified range) and if the deviation of the initial data from this steady state is small enough in a certain norm, the evolution of the system is such that its spatial density approaches a uniform constant value quasi-exponentially fast (i.e., like exp(−Ctν¯) for ν¯∈(0,1)). We take as a priori assumptions that solutions launched by such initial data exist for all times (by no means guaranteed with rVP, but a reasonable assumption since we are close to a spatially uniform state) and that the various norms in question are continuous in time (which should be a consequence of an abstract version of the Cauchy-Kovalevskaya theorem). In addition, we must assume a kind of “reverse Poincare inequality” on t...