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On the stability of blowup solutions for the critical corotational wave-map problem. (English) Zbl 1441.35071

The authors show that the finite time blowup solutions for the corotational wave-map problem constructed by the first author along with Gao, Schlag, and Tataru are stable under suitably small perturbations within the corotational class, provided that the scaling parameter \(\lambda(t)=t^{-1-\nu}\) is sufficiently close to \(t^{-1}\). The method of proof is inspired by recent work by the first author and Burzio, and takes advantage of geometric structures of the wave-map problem.

MSC:

35B44 Blow-up in context of PDEs
35B35 Stability in context of PDEs
35L71 Second-order semilinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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