The Energy-Critical Nonlinear Wave Equation with an Inverse-Square Potential
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.
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
Mathematics and Statistics
Keywords and Phrases
Energy-Critical; Ground State Threshold; Inverse-Square Potential; Nonlinear Wave Equation; Scattering
International Standard Serial Number (ISSN)
Article - Journal
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