Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on d
Abstract
In this paper, we prove polynomial growth bounds for the Sobolev norms of solutions to the fractional nonlinear Schr\"odinger equation on the torus d (d 2), following and extending a result of Joseph Thirouin on [Thi17]. The key ingredient is the establishment of Strichartz estimates for the fractional Schr\"odinger equation on d. To this end, we employ uniform estimates for oscillatory integrals to overcome the lack of uniformity that arises in higher dimensions.
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