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arXiv · 1703.00081

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

Nejla Nouaili·Hatem Zaag
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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.

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Nejla Nouaili, Hatem Zaag. 2017-12-06. Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case. https://doi.org/10.1007/s00205-017-1211-3

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