Local well-posedness for nonlinear Schrödinger equations on compact product manifolds
Abstract
We prove new local well-posedness results for nonlinear Schrödinger equations posed on a general product of spheres and tori, by the standard approach of multi-linear Strichartz estimates. To prove these estimates, we establish multi-linear bounds for the joint spectral projector associated to the Laplace–Beltrami operators on the individual sphere factors of the product manifold. To treat the particular case of the cubic NLS on a product of two spheres at critical regularity, we prove a sharp 𝐿 ∞ 𝑥 𝐿 𝑝 𝑡 estimate of the solution to the linear Schrödinger equation on the two-torus.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Journal of Differential Equations
- Volume
- 467
- Pages
- 114288–114288
- Publication date
- 5 March 2026
- Language
- EN