Titile: Long time dynamics for wave equation with potential

Abstract: We consider the long time dynamics of radial solutions to the defocusing energy critical wave equation with radial potential in 3+1 dimensions. For general potential, the equation can have a unique positive ground state and a number of excited states. In this talk, we show that for generic potential, generic radial solutions scatter to one of the stable steady states and each unstable excited state attracts a finite co-dimensional manifold of solutions. This gives affirmative answer to the soliton resolution conjecture for this particular model.

This talk is based on joint works with Hao Jia, Wilhelm Schlag and Guixiang Xu.