| Abstract: |
| This talk mainly focuses on the scattering of radial bounded solutions to focusing semi-linear wave equations with energy supercritical nonlinearity in four dimensions. We first review earlier applications of the concentration compactness and rigidity methods in energy-critical and energy-supercritical settings. As most of these results address the problem in three dimensions, we explore the unique challenges posed by analogous problems in even dimensions. We then investigate how rigidity arguments, originally developed for three dimensions and successfully generalized to higher odd dimensions, can be adapted to address these new difficulties in even-dimensional settings. |
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