论文标题
在Landau阻尼中的回声链上：自相似的解决方案和Gevrey 3作为线性稳定性阈值
On Echo Chains in Landau damping: Self-similar Solutions and Gevrey 3 as a Linear Stability Threshold
论文作者
论文摘要
我们表明，零附近自相似的非同质状态周围的线性化vlasov-poisson方程包含完整的等离子体回声机制，从而产生了Gevrey 3作为关键稳定性类别。此外，尽管爆炸爆炸，但在这里，Landau阻尼可能会持续存在：我们构建了一个关键的Gevrey规律性课程，其中力场在$ l^2 $中汇聚。因此，一方面，Landau阻尼的物理现象成立。另一方面，密度在Sobolev的规律性方面发散到无穷大。因此，``强烈阻尼''无法保持。
We show that the linearized Vlasov-Poisson equations around self-similar non-homogeneous states near zero contain the full plasma echo mechanism, yielding Gevrey 3 as a critical stability class. Moreover, here Landau damping may persist despite blow-up: We construct a critical Gevrey regularity class in which the force field converges in $L^2$. Thus, on the one hand, the physical phenomenon of Landau damping holds. On the other hand, the density diverges to infinity in Sobolev regularity. Hence, ``strong damping'' cannot hold.
