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arXiv · 2502.08812

Probabilistic global-wellposedness for the energy-supercritical Schr\"odinger equations on compact manifolds

Seynabou Gueye·Filone G. Longmou-Moffo·Mouhamadou Sy
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Abstract

We consider the nonlinear Schr\"odinger equations with a general nonlinearity power in all dimensions. We construct invariant measures concentrated on Sobolev spaces $H^s$ of singular orders, $s\leq\frac{d}{2}$. We prove almost sure global wellposedness and bounds on the growth in time of the solutions via invariant measure arguments. Our setting includes a generic compact Riemannian manifold; we specify the cases of the torus and Zoll manifolds.

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Seynabou Gueye, Filone G. Longmou-Moffo, Mouhamadou Sy. 2025-02-12. Probabilistic global-wellposedness for the energy-supercritical Schr\"odinger equations on compact manifolds. https://arxiv.org/abs/2502.08812

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