Scattering theory for the subcritical wave equation with inverse square potential

Changxing Miao ^[1] ; Ruipeng Shen ^[2] ; Tengfei Zhao ^[3]
1. [1] Institute of Applied Physics and Computational Mathematics
  
  Institute of Applied Physics and Computational Mathematics
  
  China
2. [2] Tianjin University
  
  Tianjin University
  
  China
3. [3] University of Science and Technology Beijing, China
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Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 3, 2023
Idioma: inglés
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Resumen
- We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic line method and radiation theorem, we show that the radial finite-energy solutions scatter to free waves outside of light cones. Using Morawetz estimates we then obtain the scattering theory for radial solutions with finite weighted energy initial data.