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      The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited

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      Author(s)
      Köksal, Bilge
      Özsarı, Türker
      Date
      2022-01-01
      Source Title
      Turkish Journal of Mathematics
      Print ISSN
      13000098
      Publisher
      TÜBİTAK
      Volume
      46
      Issue
      8
      Pages
      3323 - 3351
      Language
      English
      Type
      Article
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      Abstract
      In recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interiorboundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with Dirichlet/Neumann boundary conditions. © This work is licensed under a Creative Commons Attribution 4.0 International License.
      Keywords
      Fokas method
      Schrödinger equation
      Strichartz estimates
      Unified transform method
      Permalink
      http://hdl.handle.net/11693/111841
      Published Version (Please cite this version)
      https://dx.doi.org/10.55730/1300-0098.3335
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