For energy-supercritical NLS on compact manifolds, the authors claim almost sure global well-posedness on a full measure set, with an invariant flow and polynomial-in-time Sobolev growth.
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Probabilistic global-wellposedness for the energy-supercritical Schr\"odinger equations on compact manifolds
For energy-supercritical NLS on compact manifolds, the authors claim almost sure global well-posedness on a full measure set, with an invariant flow and polynomial-in-time Sobolev growth.