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arXiv · 2312.06333

Refinements of Strichartz estimates on tori and applications

Robert Schippa
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Abstract

We show trilinear Strichartz estimates in one and two dimensions on frequency-dependent time intervals. These improve on the corresponding linear estimates of periodic solutions to the Schr\"odinger equation. The proof combines decoupling iterations with bilinear short-time Strichartz estimates. Secondly, we use decoupling to show new linear Strichartz estimates on frequency dependent time intervals. We apply these in case of the Airy propagator to obtain the sharp Sobolev regularity for the existence of solutions to the modified Korteweg-de Vries equation.

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Robert Schippa. 2023-12-11. Refinements of Strichartz estimates on tori and applications. https://arxiv.org/abs/2312.06333

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