Blow-up profile for the complex Ginzburg-Landau equation

Nader Masmoudi, Hatem Zaag

Research output: Contribution to journalArticle

Abstract

We construct a solution to the complex Ginzburg-Landau equation, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite-dimensional one, and the use of index theory to conclude. Two major difficulties arise in the proof: the linearized operator around the profile is not self-adjoint and it has a second neutral mode. In the last section, the interpretation of the parameters of the finite-dimensional problem in terms of the blow-up time and the blow-up point gives the stability of the constructed solution with respect to perturbations in the initial data.

Original languageEnglish (US)
Pages (from-to)1613-1666
Number of pages54
JournalJournal of Functional Analysis
Volume255
Issue number7
DOIs
StatePublished - Oct 1 2008

Keywords

  • Blow-up profile
  • Blow-up solution
  • Complex Ginzburg-Landau equation
  • Stability

ASJC Scopus subject areas

  • Analysis

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