Local well-posedness for nonlinear Schrödinger equations on compact product manifolds

Yunfeng Zhang

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arXiv · 2503.09442

Local well-posedness for nonlinear Schrödinger equations on compact product manifolds

Yunfeng Zhang

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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 and utilize 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 $L^\infty_xL^p_t$ estimate of the solution to the linear Schrödinger equation on the two-torus.

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Yunfeng Zhang. 2026-03-02. Local well-posedness for nonlinear Schrödinger equations on compact product manifolds. https://arxiv.org/abs/2503.09442

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