### 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 language | English |
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Title of host publication | Trends in Mathematics |

Publisher | Springer International Publishing |

Pages | 179-202 |

Number of pages | 24 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Publication series

Name | Trends in Mathematics |
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ISSN (Print) | 2297-0215 |

ISSN (Electronic) | 2297-024X |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case

AU - Forcella, Luigi

AU - Fujiwara, Kazumasa

AU - Gueorguiev, Vladimir Simeonov

AU - Ozawa, Tohru

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85065816917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065816917&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-10937-0_6

DO - 10.1007/978-3-030-10937-0_6

M3 - Chapter

T3 - Trends in Mathematics

SP - 179

EP - 202

BT - Trends in Mathematics

PB - Springer International Publishing

ER -