Work

Strichartz estimates for the Schrödinger equation on compact manifolds with nonpositive sectional curvature

Year: 2025

Type: article

Abstract: We obtain improved Strichartz estimates for solutions of the Schrödinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical universal results of Burq, Gérard, and Tzvetkov (2004). More explicitly, we are able refine the arguments in the recent work of Blair and the authors (2024) to obtain no-loss L^{p}_{t}L^{q}_{x} -estimates on intervals of length \log \lambda \cdot \lambda^{-1} for all admissible pairs (p,q) when the initial data have frequencies comparable to \lambda , which, given the role of the Ehrenfest time, is the natural analog in this setting of the universal results in Burq, Gérard, and Tzvetkov (2004). We achieve this log-gain over the universal estimates by applying the Keel–Tao theorem along with improved global kernel estimates for microlocalized operators which exploit the geometric assumptions.

Source: Journal of Spectral Theory

DOI: 10.4171/jst/551

Authors: Xiaoqi Huang, Christopher D. Sogge

Institutions: Louisiana State University, Johns Hopkins University

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Awards: Variable Coefficient Fourier Analysis, Variable Coefficient Fourier Analysis