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Preprints, Working Papers, ... Year : 2023

FLAT BLOW-UP SOLUTIONS FOR THE COMPLEX GINZBURG LANDAU EQUATION

Solution explosive plate pour l'équation complexe de Ginzburg Landau

Abstract

In this paper, we consider the complex Ginzburg Landau equation Btu " p1 `iβq∆u `p1 `iδq|u| p´1 u ´αu where β, δ, α P 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.
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Dates and versions

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

Identifiers

  • HAL Id : hal-04197208 , version 1

Cite

Giao Ky Duong, Nejla Nouaili, Hatem Zaag. FLAT BLOW-UP SOLUTIONS FOR THE COMPLEX GINZBURG LANDAU EQUATION. 2023. ⟨hal-04197208⟩
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