We prove a Wong-Zakai theorem for the defocusing stochastic mass-critical nonlinear Schr¨odinger equation (NLS) on R. The main ingredient are careful mixtures of bootstrapping arguments at both deterministic and stochastic levels. Several subtleties arising from the proof mark the difference between the dispersive case and corresponding situations in SDEs and parabolic stochastic PDEs, as well as the difference between the large-n case and the limiting (n = ∞) case.

Publication:

-    SIAM Journal on Mathematical Analysis, 59, 3, 1510-1541 (2021)

Authors:

-    Chenjie Fan (Academy of Mathematics and Systems Science and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences)