Orthonormal Strichartz estimates for the Schrödinger equations with Hamiltonian on Wiener amalgam spaces
Abstract
The main objective of this paper is to investigate orthonormal Strichartz estimates for Schrödinger equation on the Wiener amalgam space 𝒲(ℱ Lp, Lq). More precisely, we first examine improvements in the time-integrability exponent of the existing Strichartz estimates established by Cordero and Nicola in \cite{NFC} for Schrödinger equations associated with ℋ+=−1/4πΔ+|x|2. We then extend these improved Strichartz estimates from a single initial datum to systems of orthonormal families, providing, to the best of our knowledge, the first results in this direction in the setting of Wiener amalgam spaces. We further extend the classical Strichartz estimates in Wiener amalgam spaces from a single initial datum to systems of orthonormal families of initial data for the Schrödinger equation associated with the operator ℋ−=−1/4πΔ−|x|2 and Hamiltonian operator of the form ℋ𝒜 = −1/4π B ∇ · ∇, where 𝒜 = 0 & B 0 & 0 ∈ Sp(d,ℝ) with B = B* and det B ≠0. A key ingredient of our approach is Stein's complex interpolation theory for Wiener amalgam spaces, combined with a duality argument inspired by the work of Frank and Sabin. As an application of these orthonormal estimates associated with ℋ+, ℋ−, and H𝒜, we establish local and small-data global well-posedness for the Hartree equation with infinitely many particles, for non-trace-class initial data.
Related
- Strichartz estimates to fractional Schrödinger equations
- Strichartz estimates for Schrödinger equations with nonlinear boundary interactions
- Critical orthonormal Strichartz estimates for Lebesgue spaces
- Critical Strichartz estimates for orthonormal systems
- Orthonormal Strichartz estimates over fractal time
BibTeX
@misc{manna2026orthonormal,
title = {{Orthonormal Strichartz estimates for the Schrödinger equations with Hamiltonian on Wiener amalgam spaces}},
author = {Ramesh Manna and Shyam Swarup Mondal and Sarthak Tiwari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29085},
eprint = {2609.29085},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29085},
}
RIS
TY - UNPB
TI - Orthonormal Strichartz estimates for the Schrödinger equations with Hamiltonian on Wiener amalgam spaces
AU - Ramesh Manna
AU - Shyam Swarup Mondal
AU - Sarthak Tiwari
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29085
UR - https://arxiv.org/abs/2609.29085
AB - The main objective of this paper is to investigate orthonormal Strichartz estimates for Schrödinger equation on the Wiener amalgam space 𝒲(ℱ L^p, L^q). More precisely, we first examine improvements in the time-integrability exponent of the existing Strichartz estimates established by Cordero and Nicola in \cite{NFC} for Schrödinger equations associated with ℋ^+=−1/4πΔ+|x|^2. We then extend these improved Strichartz estimates from a single initial datum to systems of orthonormal families, providing, to the best of our knowledge, the first results in this direction in the setting of Wiener amalgam spaces. We further extend the classical Strichartz estimates in Wiener amalgam spaces from a single initial datum to systems of orthonormal families of initial data for the Schrödinger equation associated with the operator ℋ^−=−1/4πΔ−|x|^2 and Hamiltonian operator of the form ℋ_𝒜 = −1/4π B ∇ · ∇, where 𝒜 = 0 & B 0 & 0 ∈ Sp(d,ℝ) with B = B^* and det B ≠0. A key ingredient of our approach is Stein's complex interpolation theory for Wiener amalgam spaces, combined with a duality argument inspired by the work of Frank and Sabin. As an application of these orthonormal estimates associated with ℋ^+, ℋ^−, and H_𝒜, we establish local and small-data global well-posedness for the Hartree equation with infinitely many particles, for non-trace-class initial data.
ER -