Archive for Rational Mechanics and Analysis

, Volume 228, Issue 3, pp 995–1058 | Cite as

Construction of a Blow-Up Solution for the Complex Ginzburg–Landau Equation in a Critical Case



We construct a solution for the Complex Ginzburg–Landau equation in a 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 us to prove the stability of the constructed solution.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.CEREMADE, UMR 7534Université Paris IX-Dauphine, PSL Research UniversityParisFrance
  2. 2.LAGA, CNRS (UMR 7539)Université Paris 13, Sorbonne Paris CitéVilletaneuseFrance

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