Author

Fan Xu

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Preprint Oct 2026

Global well-posedness of the energy-critical nonlinear Schr\"odinger equation on the three-dimensional torus with additive L\'evy noise

This paper establishes global well-posedness for the defocusing energy-critical nonlinear Schr\"odinger equation on the three-dimensional torus with a class of additive L\'evy noises. For arbitrary deterministic initial data in the energy space, we construct probabilistically strong solutions that are pathwise unique i...

Bin Liu, Fan Xu · 0 citations

Preprint Sep 2026

Global well-posedness and scattering for energy-critical Schrodinger equations with conservative Marcus noise

This work establishes global well-posedness for the three-dimensional defocusing energy-critical nonlinear Schr\"odinger equation with conservative linear Marcus noise. For arbitrary deterministic energy-space data, we construct a probabilistically strong solution, unique in the critical spacetime class, and prove conv...

Bin Liu, Fan Xu, Bo Yang et al. · 0 citations