Growth of Solutions to NLS on Irrational Tori

Yu Deng; Pierre Germain

doi:10.1093/imrn/rnx210

Growth of Solutions to NLS on Irrational Tori

Yu Deng, Pierre Germain

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove polynomial bounds on the H^s growth for the nonlinear Schrödinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.

Original language	English (US)
Pages (from-to)	2919-2950
Number of pages	32
Journal	International Mathematics Research Notices
Volume	2019
Issue number	9
DOIs	https://doi.org/10.1093/imrn/rnx210
State	Published - May 7 2019

ASJC Scopus subject areas

General Mathematics

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abstract = "We prove polynomial bounds on the Hs growth for the nonlinear Schr{\"o}dinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.",

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AB - We prove polynomial bounds on the Hs growth for the nonlinear Schrödinger equation set on a torus, in dimension 3, with super-cubic and sub-quintic nonlinearity. Due to improved Strichartz estimates, these bounds are better for irrational tori than they are for rational tori.

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Growth of Solutions to NLS on Irrational Tori

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