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

Miao, Changxing; Murphy, Jason; Zheng, Jiqiang

doi:10.1016/j.anihpc.2019.09.004

Miao, Changxing ¹ ; Murphy, Jason ² ; Zheng, Jiqiang ¹

¹ Institute for Applied Physics and Computational Mathematics, Beijing, China
² Missouri University of Science and Technology, Rolla, MO, USA

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 417-456.

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Résumé

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.

DOI : 10.1016/j.anihpc.2019.09.004

Mots-clés : Nonlinear wave equation, Inverse-square potential, Energy-critical, Scattering, Ground state threshold

Affiliations des auteurs :

Miao, Changxing ¹ ; Murphy, Jason ² ; Zheng, Jiqiang ¹

¹ Institute for Applied Physics and Computational Mathematics, Beijing, China
² Missouri University of Science and Technology, Rolla, MO, USA

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     title = {The energy-critical nonlinear wave equation with an inverse-square potential},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {417--456},
     publisher = {Elsevier},
     volume = {37},
     number = {2},
     year = {2020},
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     mrnumber = {4072805},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2019.09.004/}
}

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Miao, Changxing; Murphy, Jason; Zheng, Jiqiang. The energy-critical nonlinear wave equation with an inverse-square potential. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 417-456. doi : 10.1016/j.anihpc.2019.09.004. http://www.numdam.org/articles/10.1016/j.anihpc.2019.09.004/

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