Strichartz estimates for a Schr\"odinger equation on the half-line with a Neumann boundary condition

Nicola Garofalo; Gigliola Staffilani

Strichartz estimates for a Schr\"odinger equation on the half-line with a Neumann boundary condition

Analysis of PDEs 2025-07-29 v1

Authors: Nicola Garofalo , Gigliola Staffilani

Abstract

In this paper we prove some new Strichartz estimates related to the Cauchy problem for the Bessel operator on the half-line and we establish a fractal version of the Tomas-Stein restriction theorem for the Hankel transform. Then we use the proved Strichartz estimates to show global in time well-posedness for a class of nonlinear $L^2_a$ -critical problems, and local in time well-posedness in the sub-critical case.

Keywords

Strichartz estimates Schrödinger equation Neumann boundary condition Bessel operator Hankel transform well-posedness

Cite

@article{arxiv.2507.19998,
  title  = {Strichartz estimates for a Schr\"odinger equation on the half-line with a Neumann boundary condition},
  author = {Nicola Garofalo and Gigliola Staffilani},
  journal= {arXiv preprint arXiv:2507.19998},
  year   = {2025}
}

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