Abstract
In this paper we consider the Schrödinger equation with power-like nonlinearity and confining potential or without potential. This equation is known to be well-posed with data in a Sobolev space Hs if s is large enough and strongly ill-posed is s is below some critical threshold sc. Here we use the randomisation method of the inital conditions, introduced by N. Burq and N. Tzvetkov, and we are able to show that the equation admits strong solutions for data in Hs for some s<sc.
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