loading page

Local and global existence in L^{p} for the inhomogeneous nonlinear Schrödinger equation
  • deng Wang,
  • Han Yang
deng Wang
Southwest Jiaotong University

Corresponding Author:[email protected]

Author Profile
Han Yang
Southwest Jiaotong University
Author Profile

Abstract

This paper investigates the local and global existence for the inhomogeneous nonlinear Schrödinger equation with the nonlinearity λ|x|^{-b}|u|^{β}u. It is show that a global solution exists in the mass-subcritical for large data in the spaces L^{p}, p < 2 under some suitable conditions on b,β and p. The solution is established using a data-decomposition argument, two kinds of generalized Strichartz estimates in Lorentz spaces and a interpolation theorem.
18 Sep 2021Submitted to Mathematical Methods in the Applied Sciences
19 Sep 2021Submission Checks Completed
19 Sep 2021Assigned to Editor
24 Sep 2021Reviewer(s) Assigned
20 Oct 2021Review(s) Completed, Editorial Evaluation Pending
21 Oct 2021Editorial Decision: Revise Minor
27 Oct 20211st Revision Received
27 Oct 2021Submission Checks Completed
27 Oct 2021Assigned to Editor
27 Oct 2021Review(s) Completed, Editorial Evaluation Pending
27 Oct 2021Editorial Decision: Accept
15 May 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 7 on pages 3497-3513. 10.1002/mma.7997