论文标题
在围绕各向同性稳态的弗拉索夫 - 波森或爱因斯坦 - 维拉索夫系统线性化引起的运输运算符上
On the transport operators arising from linearizing the Vlasov-Poisson or Einstein-Vlasov system about isotropic steady states
论文作者
论文摘要
如果将各向同性稳态的Vlasov-Poisson或Einstein-Vlasov系统线性化，则线性操作员会产生其性能，其性能与给定稳态的线性以及非线性稳定性分析相关。我们证明，当在合适的希尔伯特空间上定义并配备了适当的定义领域时，传输操作员$ \ mathcal {t} $是Skew-Adjoint，即$ \ Mathcal {t}^{\ ast {\ ast} = - \ Mathcal {t} $。在Vlasov-Poisson情况下，我们还确定了该操作员的内核。
If the Vlasov-Poisson or Einstein-Vlasov system is linearized about an isotropic steady state, a linear operator arises the properties of which are relevant in the linear as well as nonlinear stability analysis of the given steady state. We prove that when defined on a suitable Hilbert space and equipped with the proper domain of definition this transport operator $\mathcal{T}$ is skew-adjoint, i.e., $\mathcal{T}^{\ast}=-\mathcal{T}$. In the Vlasov-Poisson case we also determine the kernel of this operator.
