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Displaying similar documents to “Harmonic maps of the hyperbolic space and development of singularities in wave maps and Yang-Mills fields”

Geometric renormalization of large energy wave maps

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...

The wave map problem. Small data critical regularity

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 ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....