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

Luigi Forcella, Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

研究成果: Chapter

抄録

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.

本文言語English
ホスト出版物のタイトルTrends in Mathematics
出版社Springer International Publishing
ページ179-202
ページ数24
DOI
出版ステータスPublished - 2019

出版物シリーズ

名前Trends in Mathematics
ISSN(印刷版)2297-0215
ISSN(電子版)2297-024X

ASJC Scopus subject areas

  • Mathematics(all)

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