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September 23, 2025Open Access

Orthonormal Strichartz estimates on torus and waveguide manifold and applications

Key Points

Establishing orthonormal Strichartz estimates enhances solutions for fractional Schrödinger equations on manifolds.
Improved $^2$ decoupling inequality in waveguide manifold leads to refined classical estimates.
Applications include demonstrating local well-posedness for Hartree equations even with non-trace class initial data.
Research insights contribute to the mathematical understanding of wave phenomena in complex geometries.

Abstract

We establish orthonormal Strichartz estimates for the fractional Schrödinger equations on torus and waveguide manifold. In the process, we also improve ² decoupling inequality and establish classical fractional Strichartz estimates on waveguide manifold. This maybe of independent interest. As an application, we establish local well-posednes for the Hartree equations with infinitely many particles with non-trace class initial data.

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Bhimani et al. (Tue,) studied this question.

www.synapsesocial.com/papers/68d4759931b076d99fa6d8eb — DOI: https://doi.org/10.48550/arxiv.2507.16712

Authors

Divyang G. Bhimani

Saumya Choudhary

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Orthonormal Strichartz estimates on torus and waveguide manifold and applications

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Authors

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