Bounds on the growth of high Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$

Antonios Kapetanios, José L. Rodrigo, Vedran Sohinger

We prove polynomial bounds on the growth of high Sobolev norms of solutions to the defocusing fractional nonlinear Schrödinger equation with cubic and Hartree-type nonlinearities i…