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Posted March 6, 2026
Last modified April 16, 2026

Applied Analysis Seminar Questions or comments?

Yunfeng Zhang, University of Cincinnati
Bilinear Eigenfunction Estimate, Anisotropic Strichartz Estimate, and Energy-Critical NLS

We prove global well-posedness for the energy-critical nonlinear Schrödinger equation on the product manifold R × S^3 with small initial data in the energy space. The first key ingredient is a sharp bilinear eigenfunction estimate for the Laplace operator on S^3, which completes the theory of multilinear eigenfunction estimates on spheres pioneered by Burq, Gérard, and Tzvetkov. Our approach relies on representation theory. The second key ingredient is a frequency-localized anisotropic Strichartz estimate on the cylinder R × T, the proof of which relies on precise measure estimates. This is joint work with Yangkendi Deng and Zehua Zhao.

Event contact: Xiaoqi Huang