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Regularity properties of the cubic biharmonic Schrödinger equation on the half line

Author

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  • Engin Başakoğlu

    (Boğaziçi University)

Abstract

In this paper we study the regularity properties of the cubic biharmonic Schrödinger equation posed on the right half line. We prove local well-posedness and obtain a smoothing result in the low-regularity spaces on the half line. In particular we prove that the nonlinear part of the solution on the half line is smoother than the initial data obtaining a full derivative gain in certain cases. Moreover, in the defocusing case, we establish global well-posedness and global smoothing in the higher order regularity spaces by making use of the global-wellposedness result of Özsarı and Yolcu (Commun Pure Appl Phys 18(6):3285–3316, 2019) in the energy space. Also this paper improves the well-posedness result of Özsarı and Yolcu (Commun Pure Appl Phys 18(6):3285–3316, 2019) in the case of cubic nonlinearity.

Suggested Citation

  • Engin Başakoğlu, 2021. "Regularity properties of the cubic biharmonic Schrödinger equation on the half line," Partial Differential Equations and Applications, Springer, vol. 2(4), pages 1-37, August.
    • Handle: RePEc:spr:pardea:v:2:y:2021:i:4:d:10.1007_s42985-021-00106-7
    DOI: 10.1007/s42985-021-00106-7
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