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...

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Bibliographic Details
Published inArchive for rational mechanics and analysis Vol. 228; no. 3; pp. 995 - 1058
Main Authors Nouaili, Nejla, Zaag, Hatem
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Subjects
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-017-1211-3