Well-posedness for a generalized derivative nonlinear Schr\"odinger equation

Masayuki Hayashi; Tohru Ozawa

doi:10.1016/j.jde.2016.08.018

Well-posedness for a generalized derivative nonlinear Schr\"odinger equation

Analysis of PDEs 2025-02-27 v2

Authors: Masayuki Hayashi , Tohru Ozawa

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Abstract

We study the Cauchy problem for a generalized derivative nonlinear Schr\"odinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces $H^1$ and $H^2$ . Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space $H^1$ .

Keywords

well-posedness global well-posedness and scattering for nonlinear dispersive equations cauchy problem

Cite

@article{arxiv.1601.04167,
  title  = {Well-posedness for a generalized derivative nonlinear Schr\"odinger equation},
  author = {Masayuki Hayashi and Tohru Ozawa},
  journal= {arXiv preprint arXiv:1601.04167},
  year   = {2025}
}

Comments

v2: minor revision; 21 pages. The assumption of Theorem 1.7 is weakened slightly. To appear in Journal of Differential Equations

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