Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case

Luigi Forcella, Kazumasa Fujiwara, Vladimir Simeonov Gueorguiev, Tohru Ozawa

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The aim of this work is to give a complete picture concerning the asymptotic behaviour of the solutions to fractional Ginzburg-Landau equation. In previous works, we have shown global well-posedness for the past interval in the case where spatial dimension is less than or equal to 3. Moreover, we have also shown blow-up of solutions for the future interval in one dimensional case. In this work, we summarise the asymptotic behaviour in the case where spatial dimension is less than or equal to 3 by proving blow-up of solutions for a future time interval in multidimensional case. The result is obtained via ODE argument by exploiting a new weighted commutator estimate.

Original languageEnglish
Title of host publicationTrends in Mathematics
PublisherSpringer International Publishing
Pages179-202
Number of pages24
DOIs
Publication statusPublished - 2019 Jan 1

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

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ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Forcella, L., Fujiwara, K., Gueorguiev, V. S., & Ozawa, T. (2019). Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case. In Trends in Mathematics (pp. 179-202). (Trends in Mathematics). Springer International Publishing. https://doi.org/10.1007/978-3-030-10937-0_6