Abstract

In this paper we prove some multilinear Strichartz estimates for solutions to the linear Schrödinger equation on the torus $\mathbb{T}^n$. Then we apply them to get some well-posedness results for the periodic nonlinear Schrödinger equation in critical $H^{s}(\mathbb{T}^n)$ spaces.

Keywords

  1. multilinear Strichartz estimates
  2. periodic NLS
  3. critical spaces
  4. global well-posedness

MSC codes

  1. 35Q55

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References

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S. Herr, D. Tataru, and N. Tzvetkov, Strichartz estimates for partially periodic solutions to Schrödinger equations in $4$d and applications, J. Reine und Angew. Math., to appear
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Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 1691 - 1703
ISSN (online): 1095-7154

History

Submitted: 29 March 2012
Accepted: 9 April 2013
Published online: 30 May 2013

Keywords

  1. multilinear Strichartz estimates
  2. periodic NLS
  3. critical spaces
  4. global well-posedness

MSC codes

  1. 35Q55

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