This paper studies the quintic nonlinear Schrödinger equation on with randomized initial data below the critical regularity for . The main result is a proof of almost sure local well-posedness given a Wiener randomization of the data in for . The argument further develops the techniques introduced in the work of Á. Bényi, T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a condition for almost sure global well-posedness.
"Almost sure local well-posedness for the supercritical quintic NLS." Tunisian J. Math. 1 (3) 427 - 453, 2019. https://doi.org/10.2140/tunis.2019.1.427