Global self-similar solutions to the cubic wave equation in 6D and corotational wave maps in 4D are orbitally stable under small critical Sobolev perturbations in forward time.
Texts Math.Berlin: Springer, 2000
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Stability of global self-similar solutions to the cubic wave equation and the wave maps equation
Global self-similar solutions to the cubic wave equation in 6D and corotational wave maps in 4D are orbitally stable under small critical Sobolev perturbations in forward time.