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

Luigi Forcella, Kazumasa Fujiwara, Vladimir Simeonov Gueorguiev, 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.

元の言語English
ホスト出版物のタイトルTrends in Mathematics
出版者Springer International Publishing
ページ179-202
ページ数24
DOI
出版物ステータスPublished - 2019 1 1

出版物シリーズ

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

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Ginzburg-Landau Equation
Global Existence
Blow-up
Fractional
Blow-up of Solutions
Less than or equal to
Interval
Asymptotic Behavior
Commutator Estimate
Weighted Estimates
Global Well-posedness

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

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. : Trends in Mathematics (pp. 179-202). (Trends in Mathematics). Springer International Publishing. https://doi.org/10.1007/978-3-030-10937-0_6

Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case. / Forcella, Luigi; Fujiwara, Kazumasa; Gueorguiev, Vladimir Simeonov; Ozawa, Tohru.

Trends in Mathematics. Springer International Publishing, 2019. p. 179-202 (Trends in Mathematics).

研究成果: Chapter

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