Refinements of Strichartz estimates on tori and applications

2023/12/11 by Robert Schippa, Schippa, Robert
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2312.06333

openalex publication_date 2023/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrödinger 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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