The cubic NLS on S² converges pointwise almost everywhere to initial data almost surely at low regularity, and a new necessary condition is given for L^p maximal estimates of the linear Schrödinger equation on S².
Bourgain,Some new estimates on oscillatory integrals, Essays on Fourier Analysis in Honor of Elias M
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On the pointwise convergence of NLS flow on $ \S^2 $
The cubic NLS on S² converges pointwise almost everywhere to initial data almost surely at low regularity, and a new necessary condition is given for L^p maximal estimates of the linear Schrödinger equation on S².