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

Nejla Nouaili (1) , Hatem Zaag (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Blow-up profile; Complex Ginzburg-Landau equation

Domaines: Equations aux dérivées partielles [math.AP]

Nejla Nouaili, Hatem Zaag. Construction of a blow-up solution for the Complex Ginzburg-Landau equation in some critical case. Archive for Rational Mechanics and Analysis, 2018, Arch. Ration. Mech. Anal., 228 (3), pp.995-1058. ⟨hal-01490862⟩