Long time dynamics of defocusing energy critical 3 + 1 dimensional wave   equation with potential in the radial case
  Using channel of energy inequalities developed by T.Duyckaerts, C.Kenig and F.Merle, we prove that, modulo a free radiation, any finite energy radial solution to the defocusing energy critical wave equation with radial potential in 3 + 1 dimensions converges to the set of steady states as time goes to infinity. For generic potentials we prove there are only finitely many steady states, and in this case modulo some free radiation the solution converges to one steady state as time goes to infinity. 
Hao Jia, Baoping Liu, Guixiang Xu
math.AP