Journal
ACTA MATHEMATICA
Volume 201, Issue 2, Pages 147-212Publisher
INT PRESS BOSTON, INC
DOI: 10.1007/s11511-008-0031-6
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Funding
- NSF
- CNRS
- ANR ONDENONLIN
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We study the energy-critical focusing non-linear wave equation, with data in the energy space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the one of the static solution W which gives the best constant in the Sobolev embedding, the following alternative holds. If the initial data has smaller norm in the homogeneous Sobolev space H 1 than the one of W, then we have global well-posedness and scattering. If the norm is larger than the one of W, then we have break-down in finite time.
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