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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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