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

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

2011-12-23

arxiv.org/abs/1112.5663v1

Mathematics

Analysis of PDEs

arXiv admin note: substantial text overlap with arXiv:1010.3799

Scientific paper

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 the natural energy space 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 time approaches infinity. In our previous paper arxiv:1010.3799 we treated the radial case, and this paper provides the natural nonradial extension of these results. However, the present paper is self-contained and in fact develops a somewhat different formalism in order to handle the more complex nonradial situation.

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