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

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Abstract

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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Authors and Affiliations

  1. CEREMADE, UMR 7534, Université Paris IX-Dauphine, PSL Research University, 75016, Paris, France

    Nejla Nouaili

  2. LAGA, CNRS (UMR 7539), Université Paris 13, Sorbonne Paris Cité, 93430, Villetaneuse, France

    Hatem Zaag

Authors
  1. Nejla Nouaili
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  2. Hatem Zaag
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Correspondence to Nejla Nouaili.

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Communicated by N. Masmoudi

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Nouaili, N., Zaag, H. Construction of a Blow-Up Solution for the Complex Ginzburg–Landau Equation in a Critical Case. Arch Rational Mech Anal 228, 995–1058 (2018). https://doi.org/10.1007/s00205-017-1211-3

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  • DOI: https://doi.org/10.1007/s00205-017-1211-3

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