October 20, 2025Open Access

On the well-posedness of time-space fractional Schrödinger equation on R^d

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Authors

YYYong Zhen YangXiangtan University YZYong ZhouZhoushan Institute of Calibration for Quality and Technology Supervision

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Implication

This analysis establishes well-posedness and dispersive estimates in fractional Schrödinger equations, highlighting the interplay of derivatives and quantum dynamics.

Key Points

Local and global well-posedness is proven for fractional Schrödinger equations, extending results to Sobolev and Lorentz-type spaces.
Novel dispersive estimates are established, addressing the derivative loss in the solution operator in comparison to classical frameworks.
Harmonic analysis tools such as interpolation techniques and the Van der Corput lemma are utilized to derive these new estimates.
The findings emphasize the relevance of fractional derivatives in the understanding of nonlocal evolution equations in quantum mechanics.

Cite This Study

Yang et al. (2025) studied this question.

synapsesocial.com/papers/68f5fcdc8d54a28a75cf22f3 https://doi.org/10.48550/arxiv.2507.04433

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Implication

This analysis establishes well-posedness and dispersive estimates in fractional Schrödinger equations, highlighting the interplay of derivatives and quantum dynamics.

On the well-posedness of time-space fractional Schrödinger equation on R^d

Discussion

Member takes

Implication

Key Points

Cite This Study

On the well-posedness of time-space fractional Schrödinger equation on R^d

Discussion

Member takes

Implication

Key Points

Cite This Study

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