Dynamics for the energy critical nonlinear wave equation in high dimensions

Abstract

T. Duyckaerts and F. Merle (2008) studied the variational structure near the ground state solution W W of the energy critical wave equation and classified the solutions with the threshold energy E ( W , 0 ) E(W,0) in dimensions d = 3 , 4 , 5 d=3,4,5 . In this paper, we extend the results to all dimensions d ≥ 6 d\ge 6 . The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of W W .