Concentration compactness for critical wave maps

Details Concentration compactness for critical wave maps Concentration compactness for critical wave maps

2009-08-18

arxiv.org/abs/0908.2474v1

Mathematics

Analysis of PDEs

261 pages, 7 figures

Scientific paper

By means of the concentrated compactness method of Bahouri-Gerard and Kenig-Merle, we prove global existence and regularity for wave maps with smooth data and large energy from 2+1 dimensions into the hyperbolic plane. The argument yields an apriori bound of the Coulomb gauged derivative components of our wave map relative to a suitable norm (which holds the solution) in terms of the energy alone. As a by-product of our argument, we obtain a phase-space decomposition of the gauged derivative components analogous to the one of Bahouri-Gerard.

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