Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case

Abstract

We construct a solution for the Complex Ginzburg-Landau equation in some critical case, which blows up in finite time $T$ only at one blow-up point. We also give a sharp description of its profile. The proof relies on the reduction of the problem to a finite dimensional one, and the use of index theory to conclude. The interpretation of the parameters of the finite dimension problem in terms of the blow-up point and time allows to prove the stability of the constructed solution.

arXiv admin note: text overlap with arXiv:1506.08306

References in corpus (1)

• Stable blow up dynamics for the 1-corotational energy critical harmonic heat flow

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