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.
On blowup in supercritical wave equations.Comm
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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.