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On Blowup Solutions to the Focusing Intercritical Nonlinear Fourth-Order Schrödinger Equation

  • Van Duong DinhEmail author
Article
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Abstract

In this paper we study dynamical properties of blowup solutions to the focusing intercritical (mass-supercritical and energy-subcritical) nonlinear fourth-order Schrödinger equation. We firstly establish the profile decomposition of bounded sequences in \(\dot{H}^{\gamma _{\text {c}}} \cap \dot{H}^2\). We also prove a compactness lemma and a variational characterization of ground states related to the equation. As a result, we obtain the \(\dot{H}^{\gamma _{\text {c}}}\)-concentration of blowup solutions with bounded \(\dot{H}^{\gamma _{\text {c}}}\)-norm and the limiting profile of blowup solutions with critical \(\dot{H}^{\gamma _{\text {c}}}\)-norm.

Keywords

Nonlinear fourth-order Schrödinger equation Blowup Concentration Limiting profile 

Notes

Acknowledgements

The author would like to express his deep thanks to his wife—Uyen Cong for her encouragement and support. He would like to thank his supervisor Prof. Jean-Marc Bouclet for the kind guidance and constant encouragement. He also would like to thank the reviewer for his/her helpful comments and suggestions.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut de Mathématiques de Toulouse UMR5219Université Toulouse CNRSToulouse Cedex 9France
  2. 2.Department of MathematicsHCMC University of PedagogyHo Chi MinhVietnam

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