Random initial data below the critical Sobolev regularity still support local solutions to the periodic nonlinear Schrodinger equation for any non-algebraic power in the mass-supercritical range.
Invariant measures for the 2d-defocusing nonlinear Schr \"o dinger equation
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Almost sure local well-posedness for the nonlinear Schr\"odinger equations on $\Bbb T^d$ with non-algebraic nonlinearity
Random initial data below the critical Sobolev regularity still support local solutions to the periodic nonlinear Schrodinger equation for any non-algebraic power in the mass-supercritical range.