Orthonormal Strichartz estimates on torus and waveguide manifold and applications

2025/07/22 by Divyang G. Bhimani, Bhimani, Divyang G., Saumya Choudhary +1
Mathematics · #35B45 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2507.16712

openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish new orthonormal Strichartz estimates for the fractional Schrödinger equations on torus \mathbb T and waveguide manifold \mathbb Rⁿ× \mathbb T^m. We generalizes the result of Nakamura [42] on torus; while this is the first result on the waveguide manifold. The main novelty in this paper is the derivation of various kernel estimates associated to the fractional Schrödinger equations. Our kernel estimate generalizes the classical dispersive estimate on torus due to Kenig-Ponce-Vega [35]. On the other hand, we obtain new ℓ² decoupling inequality for degeneracy type surfaces to treat the case of waveguide manifold; which maybe of independent interest and complements several known results. As an application, we establish local and small data global well-posednes for the Hartree equation with infinitely many particles with non-trace class initial data.

Citations

• Strichartz estimates for orthonormal systems on compact manifolds
• Orthonormal Strichartz estimate for dispersive equations with potentials
• Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
• The orthonormal Strichartz inequality on torus
• On the Strichartz estimates for orthonormal systems of initial data with regularity
• The Stein-Tomas inequality in trace ideals
• The proof of the l² Decoupling Conjecture
• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations
• Scale invariant Strichartz estimates on tori and applications
• Decouplings for curves and hypersurfaces with nonzero Gaussian curvature
• Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates
• Well-posedness and Ill-posedness for the cubic fractional Schrödinger equations

Related

• Strichartz estimates for orthonormal systems on compact manifolds
• Strichartz estimates for the Schrödinger equation on compact manifolds with nonpositive sectional curvature
• Orthonormal Strichartz estimate for dispersive equations with potentials
• Bilinear Strichartz estimates on rescaled waveguide manifolds with applications
• On Strichartz estimate for many body Schrödinger equation in the waveguide setting