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

Joachim Krieger | Zendy; Kenji Nakanishi | Zendy; Wilhelm Schlag | Zendy

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

Author(s) -

Joachim Krieger,

Kenji Nakanishi,

Wilhelm Schlag

Publication year - 2012

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.2423

Subject(s) - energy (signal processing) , physics , ground state , nonlinear system , wave equation , dynamics (music) , equation of state , scattering , state (computer science) , mathematical analysis , classical mechanics , mathematics , quantum mechanics , acoustics , algorithm

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 H(over dot) x 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 -> +/-infinity.

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