发表机构
Zhejiang University of Technology; Zhejiang Normal University（浙江工业大学; 浙江师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立非陷获渐近双曲流形上Klein-Gordon方程的时间全局Strichartz估计，将其应用于半线性方程的小数据全局存在性与散射研究。
AI 中文摘要
本文针对非陷获渐近双曲流形上的Klein-Gordon方程，建立了时间全局的Strichartz估计。该结果是Sire、Sogge、Wang和Zhang针对平移波动方程所得全局Strichartz估计的正质量对应结果，且恢复了相同的容许对范围。主要新特征在于低频分析：正质量改变了谱相位，产生了不同的色散机制。将所得低频估计与微局部化高频估计相结合，得到了完整的全局Strichartz估计。作为应用，我们获得了幂型及特定导数半线性方程的小数据全局存在性与散射结果，还得到了一类光滑半线性方程的小数据全局存在性，且无需施加零条件。
英文摘要
In this paper, we establish global-in-time Strichartz estimates for Klein-Gordon equations on non-trapping asymptotically hyperbolic manifolds. Our result is a positive-mass counterpart of the global Strichartz estimates of Sire, Sogge, Wang, and Zhang for shifted wave equations, and recovers the same range of admissible pairs. The main new feature is the low-frequency analysis, where the positive mass changes the spectral phase and leads to a different dispersive mechanism. Combining the resulting low-frequency estimates with microlocalized high-frequency estimates yields the full global Strichartz estimates. As applications, we obtain small-data global existence and scattering for power-type and certain derivative semilinear equations, as well as small-data global existence for a class of smooth semilinear equations without imposing a null condition.
Comments28 pages, 1 figures. All comments are welcome
