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

Date
2022-01-01
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Source Title
Turkish Journal of Mathematics
Print ISSN
13000098
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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.

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Keywords
Fokas method, Schrödinger equation, Strichartz estimates, Unified transform method
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Published Version (Please cite this version)