Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on \T^d

Jiajun Wang

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arXiv · 2603.24906

Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on \T^d

Jiajun Wang

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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 \T^d (d \ge 2), following and extending a result of Joseph Thirouin on \T [Thi17]. The key ingredient is the establishment of Strichartz estimates for the fractional Schr\"odinger equation on \T^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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Jiajun Wang. 2026-03-26. Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on \T^d. https://arxiv.org/abs/2603.24906

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