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On the Focusing Energy-Critical 3D Quintic Inhomogeneous NLS

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Advances in Harmonic Analysis and Partial Differential Equations

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We consider the focusing energy-critical inhomogeneous nonlinear Schrödinger equation:

$$\displaystyle iu_t + \Delta u + g|u|{ }^4u = 0, \;\;u(0) \in \dot {H}^1,\;\; g \ge 0. $$

On the road map of Kenig–Merle [20] we show the global well-posedness and scattering of radial solutions under scaling, variational, and rigidity assumptions for g. We also provide sharp finite time blowup results for nonradial and radial solutions. For this we utilize the localized virial identity.

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Acknowledgements

The authors would like to thank the referee for careful reading. This work was supported by NRF-2018R1D1A3B07047782 (Republic of Korea).

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Authors and Affiliations

  1. Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju, Republic of Korea

    Yonggeun Cho

  2. Department of Mathematics, Jeonbuk National University, Jeonju, Republic of Korea

    Kiyeon Lee

Authors
  1. Yonggeun Cho
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  2. Kiyeon Lee
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Correspondence to Kiyeon Lee .

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Editors and Affiliations

  1. Department of Mathematics, University of Pisa, Pisa, Italy

    Vladimir Georgiev

  2. Department of Applied Physics, Waseda University, Tokyo, Japan

    Tohru Ozawa

  3. Department of Mathematics, Ghent University, Gent, Belgium

    Michael Ruzhansky

  4. Department of Mathematics, University of Stuttgart, Stuttgart, Germany

    Jens Wirth

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Cho, Y., Lee, K. (2020). On the Focusing Energy-Critical 3D Quintic Inhomogeneous NLS. In: Georgiev, V., Ozawa, T., Ruzhansky, M., Wirth, J. (eds) Advances in Harmonic Analysis and Partial Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-58215-9_6

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