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arXiv · 0911.4745

Dynamics for the energy critical nonlinear wave equation in high dimensions

Dong Li·Xiaoyi Zhang
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Abstract

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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Dong Li, Xiaoyi Zhang. 2009-11-25. Dynamics for the energy critical nonlinear wave equation in high dimensions. https://arxiv.org/abs/0911.4745

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