| Abstract: |
| In this talk, we consider the defocusing energy critical wave equation with a trapping potential. When the potential decays fast enough, it is easy to show that all finite energy solutions exist globally, hence our main interest is to describe the long time dynamics. In the radial case, our previous works gave a complete answer and we were able to classify all the long time dynamics. Here we partly extend previous result to the nonradial case, and show that the set of initial data for which solutions scatter to an unstable excited state forms a finite co-dimensional path connected C1 manifold in the energy space. This gives us a better understanding of the non-generic behavior of solutions, with the generic behavior left as an open problem. |
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