Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane

E. Compaan, N. Tzirakis

Research output: Contribution to journalArticlepeer-review

Abstract

We obtain an almost sharp local well–posedness result for the biharmonic equation on the quarter plane. In addition, we prove that the nonlinear part of the solution is significantly smoother than the linear part. We use a variant of the restricted norm method of Bourgain adapted to initial–boundary value problems. Our result extends the recent results in Capistrano-Filho et al. (Pacific J Math 309(1):35–70, 2020), Ozsari and Yolcu (Commun Pure Appl Anal 18(6):3285–3316, 2019) and Basakoglu (Part Differ Equ Appl 2(4):37, 2021). It is sharp in the sense that we obtain the well–posedness threshold that was obtained for the full line problem in Seong (J Math Anal Appl 504(1):125342, 2021), with the exception of the endpoint.

Original languageEnglish (US)
Article number48
JournalPartial Differential Equations and Applications
Volume4
Issue number6
DOIs
StatePublished - Dec 2023

Keywords

  • Biharmonic Schrödinger
  • Initial–boundary value problems
  • Restricted norm method

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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