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arXiv · 2506.05493

Orthonormal Strichartz estimates for Dunkl-Schr\"{o}dinger equation of initial data with Sobolev regularity

Guoxia Feng·Shyam Swarup Mondal·Manli Song·Huoxiong Wu
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Abstract

Let $\Delta_\kappa$ be the Dunkl-Laplacian on $\mathbb{R}^n$. The main aim of this paper is to investigate the orthonormal Strichartz estimates for the Schr\"odinger equation with initial data from the homogeneous Dunkl-Sobolev space $\dot{H}_\kappa^s (\mathbb{R}^n)$. Our approach is based on restricted weak-type orthonormal estimates, frequency-localized estimates for the Dunkl-Schr\"odinger propagator $e^{it\Delta_\kappa}$, and a series of successive real and complex interpolation techniques.

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Guoxia Feng, Shyam Swarup Mondal, Manli Song, Huoxiong Wu. 2025-06-05. Orthonormal Strichartz estimates for Dunkl-Schr\"{o}dinger equation of initial data with Sobolev regularity. https://arxiv.org/abs/2506.05493

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