Abstract
We consider the cubic nonlinear Schrödinger equation (NLS) on ℝ3 with randomized initial data. In particular, we study an iterative approach based on a partial power series expansion in terms of the random initial data. By performing a fixed point argument around the second order expansion, we improve the regularity threshold for almost sure local wellposedness from our previous work. We further investigate a limitation of this iterative procedure. Finally, we introduce an alternative iterative approach, based on a modified expansion of arbitrary length, and prove almost sure local wellposedness of the cubic NLS in an almost optimal regularity range with respect to the original iterative approach based on a power series expansion.
Original language  English 

Pages (fromto)  114160 
Number of pages  47 
Journal  Transactions of the American Mathematical Society: Series B 
Volume  6 
DOIs  
Publication status  Published  4 Mar 2019 
Keywords
 Partial differential equations
 Probability theory and stochastic processes
ASJC Scopus subject areas
 Mathematics(all)
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Profiles

Oana Pocovnicu
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Mathematics  Associate Professor
Person: Academic (Research & Teaching)