Nonlinear Schrödinger equations on compact Zoll manifolds with odd growth

Jian Wei Yang

doi:10.1007/s11425-014-4947-3

Nonlinear Schrödinger equations on compact Zoll manifolds with odd growth

Jian Wei Yang^*

^*Corresponding author for this work

China Academy of Engineering Physics

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

4 Citations (Scopus)

Abstract

We study nonlinear Schrödinger equations on Zoll manifolds with nonlinear growth of the odd order. It is proved that local uniform well-posedness are valid in the H^s-subcritical setting according to the scaling invariance, apart from the cubic growth in dimension two. This extends the results by Burq et al. (2005) to higher dimensions with general nonlinearities.

Original language	English
Pages (from-to)	1023-1046
Number of pages	24
Journal	Science China Mathematics
Volume	58
Issue number	5
DOIs	https://doi.org/10.1007/s11425-014-4947-3
Publication status	Published - 1 May 2015
Externally published	Yes

Keywords

Bourgain space
Schrödinger equations
Zoll manifolds

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10.1007/s11425-014-4947-3

Cite this

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title = "Nonlinear Schr{\"o}dinger equations on compact Zoll manifolds with odd growth",

abstract = "We study nonlinear Schr{\"o}dinger equations on Zoll manifolds with nonlinear growth of the odd order. It is proved that local uniform well-posedness are valid in the Hs-subcritical setting according to the scaling invariance, apart from the cubic growth in dimension two. This extends the results by Burq et al. (2005) to higher dimensions with general nonlinearities.",

keywords = "Bourgain space, Schr{\"o}dinger equations, Zoll manifolds",

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AB - We study nonlinear Schrödinger equations on Zoll manifolds with nonlinear growth of the odd order. It is proved that local uniform well-posedness are valid in the Hs-subcritical setting according to the scaling invariance, apart from the cubic growth in dimension two. This extends the results by Burq et al. (2005) to higher dimensions with general nonlinearities.

KW - Bourgain space

KW - Schrödinger equations

KW - Zoll manifolds

UR - https://www.scopus.com/pages/publications/84939995545

U2 - 10.1007/s11425-014-4947-3

DO - 10.1007/s11425-014-4947-3

M3 - Article

AN - SCOPUS:84939995545

SN - 1674-7283

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JO - Science China Mathematics

JF - Science China Mathematics

IS - 5

ER -

Nonlinear Schrödinger equations on compact Zoll manifolds with odd growth

Abstract

Keywords

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