Author

Jia-Hao Tan

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Preprint Sep 2026

Sharp lower bounds for the periodic maximal Schr\"odinger operator in higher dimensions

We prove sharp lower bounds for the Schr\"odinger maximal function on the torus T^d for all dimensions d at least 2, and as a corollary obtain sharp regularity conditions for pointwise convergence of the periodic Schr\"odinger equation. Combined with sufficiency results established by Compaan-Luc\'a-Staffilani, this yi...

Inbo Gottlieb Fenves, Jia-Hao Tan · 0 citations

Open access Aug 2026

Numerical Investigation of Gas Dispersion, Drag-Coefficient Distribution, and Mixing Performance in a Rushton-Turbine Stirred Tank Using a Euler–Euler Model

Gas dispersion and liquid circulation are critical factors governing the performance of gas–liquid stirred tanks, yet the coupled effects of operating conditions and impeller geometry on hydrodynamic behavior remain insufficiently understood. In this study, a Euler–Euler two-fluid model coupled with the standard k–ε tu...

Li-Xia Hu, Di-Hao Xie, Jia-Hao Tan et al. · Processes · 0 citations

Preprint Aug 2026

Maximal estimates for perturbations of the Schr\"odinger operator on $\mathbb{T}^d$

We study $L^p_x L^\infty_t$ maximal estimates for exponential sums associated to $C^2$ graph hypersurfaces, motivated by Schr\"odinger maximal estimates on $\mathbb{T}^d$. We show that the conjectured maximal estimate for the periodic Schr\"odinger equation fails when one allows small perturbations of the paraboloid, w...

Inbo Gottlieb Fenves, Jia-Hao Tan · 0 citations