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Scattering for the 3D Gross–Pitaevskii Equation

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Abstract

We study the Cauchy problem for the 3D Gross–Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gérard (Ann. Inst. H. Poincaré Anal. Non Linéaire 23(5):765–779, 2006). In this paper we prove scattering for small data in the same space with some additional angular regularity, and in particular in the radial case we obtain small energy scattering.

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Authors and Affiliations

  1. School of Mathematical Sciences, Monash University, Melbourne, VIC, 3800, Australia

    Zihua Guo

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Zaher Hani

  3. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, 565-0871, Japan

    Kenji Nakanishi

Authors
  1. Zihua Guo
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  2. Zaher Hani
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  3. Kenji Nakanishi
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Corresponding author

Correspondence to Zihua Guo.

Additional information

Communicated by W. Schlag

Z.G. is partially supported by ARC DP170101060. Z.H. was supported by a Sloan Fellowship, National Science Foundation Grant DMS-1600561, and a startup fund from Georgia Institute of Technology.

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Guo, Z., Hani, Z. & Nakanishi, K. Scattering for the 3D Gross–Pitaevskii Equation. Commun. Math. Phys. 359, 265–295 (2018). https://doi.org/10.1007/s00220-017-3050-3

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  • DOI: https://doi.org/10.1007/s00220-017-3050-3

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