JournalsaihpcVol. 37, No. 2pp. 417–456

The energy-critical nonlinear wave equation with an inverse-square potential

  • Changxing Miao

    Institute for Applied Physics and Computational Mathematics, Beijing, China

  • Jason Murphy

    Missouri University of Science and Technology, Rolla, MO, USA

  • Jiqiang Zheng

    Institute for Applied Physics and Computational Mathematics, Beijing, China
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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.

Cite this article

Changxing Miao, Jason Murphy, Jiqiang Zheng, The energy-critical nonlinear wave equation with an inverse-square potential. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 2, pp. 417–456

DOI 10.1016/J.ANIHPC.2019.09.004