## 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

### Keywords:

critical wave equation
Full Text:

### References:

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