电荷转移模型的Lahartz估计
Strichartz Estimates for Charge Transfer Models
摘要：
本文证明了在$\mathbb{R}^{3}$中标量电荷转移模型散射态的Ehartz估计。基于证明\cite{CM,RSS}的Eschenhartz估计的思想，我们还证明了整个演化的能量是有界的，与时间无关，而不使用相空间方法，例如，在\cite{Graf}。可以很容易地将我们的论点推广到$n\geq3$的$\mathbb{R}^{n}$。最后，在最后一节中，我们讨论了这些结果的推广到$\mathbb{R}^{3}$中的矩阵电荷转移模型。
英文摘要：
In this note, we prove Strichartz estimates for scattering states of scalar charge transfer models in $\mathbb{R}^{3}$. Based on the idea of the proof of Strichartz estimates which follows \cite{CM,RSS}, we also show the energy of the whole evolution is bounded independently of time without using the phase space method, for example, in \cite{Graf}. One can easily generalize our argument to $\mathbb{R}^{n}$ for $n\geq3$. Finally, in the last section, we discuss the extension of these results to matrix charge transfer models in $\mathbb{R}^{3}$.
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