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Strichartz estimates for non-degenerate Schrödinger equations
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2020-04-01 , DOI: 10.1002/mana.201800148
Kouichi Taira 1
Affiliation  

We consider Schr\"odinger equation with a non-degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schr\"odinger equation without loss of derivatives including the endpoint case. In contrast to the Riemannian metric case, we need the additional assumptions for the well-posedness of our Schr\"odinger equation and for proving Strichartz estimates without loss.

中文翻译:

非退化薛定谔方程的 Strichartz 估计

我们考虑在欧几里得空间上具有非退化度量的 Schr\"odinger 方程。我们研究 Schr\"odinger 方程的局部时间 Strichartz 估计,而不会丢失包括端点情况在内的导数。与黎曼度量情况相反,我们需要额外的假设来确定我们的 Schr\"odinger 方程的适定性,并在没有损失的情况下证明 Strichartz 估计。
更新日期:2020-04-01
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