The Energy-Critical Nonlinear Wave Equation with an Inverse-Square Potential

Author

Changxing Miao
Jason Murphy, Missouri University of Science and TechnologyFollow
Jiqiang Zheng

Abstract

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.

Recommended Citation

C. Miao et al., "The Energy-Critical Nonlinear Wave Equation with an Inverse-Square Potential," Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, vol. 37, no. 2, pp. 417 - 456, Elsevier Masson SAS, Mar 2020.

The definitive version is available at https://doi.org/10.1016/j.anihpc.2019.09.004

Department(s)

Mathematics and Statistics

Keywords and Phrases

Energy-Critical; Ground State Threshold; Inverse-Square Potential; Nonlinear Wave Equation; Scattering

International Standard Serial Number (ISSN)

0294-1449

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Elsevier Masson SAS, All rights reserved.

Publication Date

Mar-Apr 2020