Small Data Global Well-Posedness and Scattering for the Inhomogeneous Nonlinear Schrödinger Equation in

  • JinMyong An

    Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
  • JinMyong Kim

    Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
Small Data Global Well-Posedness and Scattering for the Inhomogeneous Nonlinear Schrödinger Equation in $H^s(\mathbb{R}^n)$ cover

A subscription is required to access this article.

Abstract

We consider the Cauchy problem for the inhomogeneous nonlinear Schrödinger (INLS) equation

where , and is a nonlinear function that behaves like with and . We prove that the Cauchy problem of the INLS equation is globally well-posed in if the initial data is sufficiently small and , where and if , if . Our global well-posedness result improves the one of Guzmán [Nonlinear Anal. Real World Appl. 37 (2017), 249–286] by extending the validity of and . In addition, we also have the small data scattering result.

Cite this article

JinMyong An, JinMyong Kim, Small Data Global Well-Posedness and Scattering for the Inhomogeneous Nonlinear Schrödinger Equation in . Z. Anal. Anwend. 40 (2021), no. 4, pp. 453–475

DOI 10.4171/ZAA/1692