Dynamics for the energy critical nonlinear wave equation in high dimensions

Details Dynamics for the energy critical nonlinear wave equation in high dimensions Dynamics for the energy critical nonlinear wave equation in high dimensions

2009-11-25

arxiv.org/abs/0911.4745v1

Mathematics

Analysis of PDEs

24 pages, to appear in Transactions AMS

Scientific paper

In the work by T. Duyckaerts and F. Merle, they studied the variational structure near the ground state solution $W$ of the energy critical wave equation and classified the solutions with the threshold energy $E(W,0)$ in dimensions $d=3,4,5$. In this paper, we extend the results to all dimensions $d\ge 6$. 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 $W$.

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