Decay estimates for the critical semilinear wave equation

Hajer Bahouri; Jalal Shatah

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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....

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