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Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces

Authors
  • Ruzhansky, M
  • Wang, B
  • Zhang, H
Publication Date
Sep 08, 2015
Identifiers
DOI: 10.1016/j.matpur.2015.09.005
OAI: oai:spiral.imperial.ac.uk:10044/1/42532
Source
Spiral - Imperial College Digital Repository
Keywords
License
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Abstract

The local well-posedness with small data in Hs(Rn)(s⩾3+max⁡(n/2,1+)) for the Cauchy problem of the fourth order nonlinear Schrödinger equations with the third order derivative nonlinear terms were obtained by Huo and Jia [17]. In this paper we show its global well-posedness with small data in the modulation space View the MathML source and in Sobolev spaces Hn/2+7+/2. For a special nonlinear term containing only one third order derivative, we can show its global well posedness in View the MathML source and H(n+1+)/2.

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