Weak compactness of wave maps and harmonic maps
Stefan Müller, Michael Struwe, Alexandre Freire (1998)
Annales de l'I.H.P. Analyse non linéaire
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Stefan Müller, Michael Struwe, Alexandre Freire (1998)
Annales de l'I.H.P. Analyse non linéaire
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Terence Tao (2004)
Journées Équations aux dérivées partielles
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There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy...
Michael Struwe (1997)
Journées équations aux dérivées partielles
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Yi Zhou (1999)
Annales de l'I.H.P. Analyse non linéaire
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Igor Rodnianski (2005-2006)
Séminaire Bourbaki
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The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....
Hajer Bahouri, Jalal Shatah (1998)
Annales de l'I.H.P. Analyse non linéaire
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