Dynamics of Partial Differential Equations

Volume 15 (2018)

Number 3

Blow-up for self-interacting fractional Ginzburg–Landau equation

Pages: 175 – 182

DOI: https://dx.doi.org/10.4310/DPDE.2018.v15.n3.a1

Authors

Kazumasa Fujiwara (Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Pisa, Italy)

Vladimir Georgiev (Department of Mathematics, University of Pisa, Italy; and Faculty of Science and Engineering, Waseda University, Tokyo, Japan)

Tohru Ozawa (Department of Applied Physics, Waseda University, Tokyo, Japan)

Abstract

The blow-up of solutions for the Cauchy problem of fractional Ginzburg–Landau equation with non-positive nonlinearity is shown by an ODE argument. Moreover, in one dimensional case, the optimal lifespan estimate for size of initial data is obtained.

Keywords

fractional Ginzburg–Landau equation, blow-up

2010 Mathematics Subject Classification

Primary 35Q40. Secondary 35Q55.

Full Text (PDF format)

The first author was partly supported by the Japan Society for the Promotion of Science, Grant-in-Aid for JSPS Fellows no 16J30008 and Top Global University Project of Waseda University.

The second author was supported in part by INDAM, GNAMPA - Gruppo Nazionale per l’Analisi Matematica, la Probabilita e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University.

The third author was supported by Grant-in-Aid for Scientific Research (A) Number 26247014.

Received 2 October 2017

Published 29 May 2018