FLAT BLOW-UP SOLUTIONS FOR THE COMPLEX GINZBURG LANDAU EQUATION - Observatoire de la Cote d'Azur
Processing math: 100%
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2024

FLAT BLOW-UP SOLUTIONS FOR THE COMPLEX GINZBURG LANDAU EQUATION

Solution explosive plate pour l'équation complexe de Ginzburg Landau

Giao Ky Duong
Hatem Zaag

Résumé

In this paper, we consider the complex Ginzburg Landau equation ut=(1+iβ)Δu+(1+iδ)|u|p1uαu where β, δ, α are in R. The study aims to investigate the finite time blowup phenomenon. In particular, for fixed β P R, the existence of finite time blowup solutions for an arbitrary large |δ| is still unknown. Especially, Popp et al [24] formally conjectured that there is no blowup (collapse) in such case. In this work, considered as a breakthrough, we give a counter example to this conjecture. We show the existence of blowup solutions in one dimension with δ arbitrarily given and β " 0. The novelty is based on two main contributions: an investigation of a new blowup scaling (flat blowup regime) and a suitable modulation.
Fichier principal
Vignette du fichier
Flat_Blowup_CGL_delta_august_2023.pdf (545.33 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04197208 , version 1 (05-09-2023)

Identifiants

Citer

Giao Ky Duong, Nejla Nouaili, Hatem Zaag. FLAT BLOW-UP SOLUTIONS FOR THE COMPLEX GINZBURG LANDAU EQUATION. Archive for Rational Mechanics and Analysis, 2024, 248 (6), pp.117. ⟨10.1007/s00205-024-02052-1⟩. ⟨hal-04197208⟩
59 Consultations
23 Téléchargements

Altmetric

Partager

More