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

Engin Başakoğlu ()
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Engin Başakoğlu: Boğaziçi University

Partial Differential Equations and Applications, 2021, vol. 2, issue 4, 1-37

Abstract: 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.

Keywords: Initial boundary value problem; Local wellposedness; Global wellposedness; Smoothing; 35G30; 35Q55 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00106-7

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