On the energy critical focusing non-linear wave equation
Carlos E. Kenig, Frank Merle (2006-2007)
Séminaire Équations aux dérivées partielles
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Displaying similar documents to “Decay estimates for the critical semilinear wave equation”
On the energy critical focusing non-linear wave equation
The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space
M. Nakamura, T. Ozawa (1999)
Annales de l'I.H.P. Physique théorique
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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 , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory....
Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills Problems
Pierre Raphaël, Igor Rodnianski (2008-2009)
Séminaire Équations aux dérivées partielles
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This note summarizes the results obtained in []. We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the target in all homotopy classes and for the equivariant critical Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.
On the regularity properties of non-linear wave equations
S. Klainerman, Matei Machedon (1997)
Journées équations aux dérivées partielles
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The global Cauchy problem for the non linear Klein-Gordon equation-II
J. Ginibre, G. Velo (1989)
Annales de l'I.H.P. Analyse non linéaire
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