Decay estimates for the critical semilinear wave equation
Hajer Bahouri, Jalal Shatah (1998)
Annales de l'I.H.P. Analyse non linéaire
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Hajer Bahouri, Jalal Shatah (1998)
Annales de l'I.H.P. Analyse non linéaire
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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.
Michael Struwe (2013)
Journal of the European Mathematical Society
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Extending our previous work, we show that the Cauchy problem for wave equations with critical exponential nonlinearities in 2 space dimensions is globally well-posed for arbitrary smooth initial data.
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....
Matthew D. Blair, Hart F. Smith, Christopher D. Sogge (2009)
Annales de l'I.H.P. Analyse non linéaire
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Georgiev, V. (1996)
Serdica Mathematical Journal
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∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology. In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was...
Jing Lu (2013)
Applicationes Mathematicae
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We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].