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Scattering Theory for the Defocusing Fourth Order NLS with Potentials

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Abstract

Based on the endpoint Strichartz estimates for the fourth order Schrödinger equation with potentials for n ≥ 5 by [Feng, H., Soffer, A., Yao, X.: Decay estimates and Strichartz estimates of the fourth-order Schrödinger operator. J. Funct. Anal., 274, 605–658 (2018)], in this paper, the authors further derive Strichartz type estimates with gain of derivatives similar to the one in [Pausader, B.: The cubic fourth-order Schrödinger equation. J. Funct. Anal., 256, 2473–2517 (2009)]. As their applications, we combine the classical Morawetz estimate and the interaction Morawetz estimate to establish scattering theory in the energy space for the defocusing fourth order NLS with potentials and pure power nonlinearity \(1 + \frac{8}{n} < p < 1 + \frac{8}{{n - 4}}\) in dimensions n ≥ 7.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, P. R. China

    Hong Liang Feng

  2. School of Mathematics and Statistics and Hubei Province Key Laboratory of Mathematical Physics, Central China Normal University, Wuhan, 430079, P. R. China

    Hua Wang & Xiao Hua Yao

Authors
  1. Hong Liang Feng
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  2. Hua Wang
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  3. Xiao Hua Yao
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Correspondence to Xiao Hua Yao.

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Feng, H.L., Wang, H. & Yao, X.H. Scattering Theory for the Defocusing Fourth Order NLS with Potentials. Acta. Math. Sin.-English Ser. 34, 773–786 (2018). https://doi.org/10.1007/s10114-018-7343-z

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  • DOI: https://doi.org/10.1007/s10114-018-7343-z

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