Strichartz estimates for non elliptic Schroedinger equations on compact manifolds
Strichartz estimates for non elliptic Schroedinger equations on compact manifolds
复制标题
紧流形上非椭圆薛定谔方程的 Strichartz 估计
DOI：
10.1080/03605302.2015.1010211
复制
发表时间：
2015
影响因子：
1.9
通讯作者：
N. Tzvetkov
中科院分区：
文献类型：
--
作者：
H. Mizutani;N. Tzvetkov
本文考虑紧致流形上的薛定谔方程，该流形具有可能退化的度量。我们证明了带导数损失的Schmidhartz估计。导数的损失率取决于度量的退化程度。对于非退化情形，作为主要结果的应用，我们得到了与椭圆情形相同的Eschenhartz估计。这将Burq-Gérard-Tzvetkov证明的黎曼度量的Eschhartz估计推广到非椭圆情形，并改进了Salort在退化情形下的结果。我们还研究了3×3情况下结果的最优性。
In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊3× 𝕊3.