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arXiv · 2411.06104

Regularity of Solution of the Schr\"odinger Equation on Symmetric Space

Pratyoosh Kumar·Manali Sajjan
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Abstract

In this article, we investigate the behavior of solutions \( u(x,t) \) to the fractional Schr\"odinger equation on rank symmetric spaces of non-compact type. We proved that as time \( t \) approaches $0$, then $u(x,t)$ converges pointwise almost everywhere to the initial radial data \( f \), provided that \( f \in H^s(\mathbb{X}) \) with \( s > \frac{1}{2} \). This result extends Sj\"olin's results in this setting.

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Pratyoosh Kumar, Manali Sajjan. 2024-11-09. Regularity of Solution of the Schr\"odinger Equation on Symmetric Space. https://arxiv.org/abs/2411.06104

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