The energy-critical nonlinear wave equation with an inverse-square potential期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Affiliation:	1. Institute for Applied Physics and Computational Mathematics, Beijing, China;2. Missouri University of Science and Technology, Rolla, MO, USA;1. Department of Mathematics, University of California, Santa Barbara, CA, United States of America;2. Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States of America;1. Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany;2. Ruhr-Universität Bochum, Fakultät für Mathematik, Gebäude NA 4/33, D-44801 Bochum, Germany;1. Université Bourgogne Franche-Comté, CNRS, IMB, F-21000 Dijon, France;2. Université de Lorraine, CNRS, IECL, F-54000 Nancy, France;1. Maxwell Institute for Mathematical Sciences, Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom;2. Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom

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.

Keywords:	Nonlinear wave equation Inverse-square potential Energy-critical Scattering Ground state threshold
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