Global dynamics of the nonradial energy-critical wave equation above the ground state energy

Joachim Krieger; Kenji Nakanishi; Wilhelm Schlag

doi:10.3934/dcds.2013.33.2423

Article Contents

2013, Volume 33, Issue 6: 2423-2450. Doi: 10.3934/dcds.2013.33.2423

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Global dynamics of the nonradial energy-critical wave equation above the ground state energy

1.
Bâtiment des Mathématiques, EPFL, Station 8, CH-1015 Lausanne
2.
Department of Mathematics, Kyoto University, Kyoto 606-8502
3.
Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, IL 60615

Received: December 31, 2011

Revised: July 31, 2012

Published: June 2013

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Abstract

In this paper we establish the existence of certain classes of solutions to the energy critical nonlinear wave equation in dimensions $3$ and $5$ assuming that the energy exceeds the ground state energy only by a small amount. No radial assumption is made. We find that there exist four sets in $\dot H^{1}\times L^{2}$ with nonempty interiors which correspond to all possible combinations of finite-time blowup on the one hand, and global existence and scattering to a free wave, on the other hand, as $t → ±∞$.

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Mathematics Subject Classification: 35L05, 35B40.

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