@article{214432bc5eb241faab028cdd408ab3f2,
title = "Local well-posedness and blow-up for the half ginzburg-landau-kuramoto equation with rough coefficients and potential",
abstract = "We study the initial value problem for the half Ginzburg-Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coefficients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is shown by an ODE argument. The key tools in the proof are appropriate commutator estimates and the essential self-adjointness of the symmetric uniformly elliptic operator with rough metric and potential type perturbation.",
keywords = "Blow-up, Commutator estimate, Fractional Ginzburg-Landau equation",
author = "Luigi Forcella and Kazumasa Fujiwara and Vladimir Georgiev and Tohru Ozawa",
note = "Funding Information: K. F. was partly supported by Top Global University Project of Waseda University. V. G. was supported in part by Project 2017 “Problemi stazionari e di evoluzione nelle equazioni di campo nonlineari” of INDAM, GNAMPA – Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and Top Global University Project, Waseda University, by the University of Pisa, Project PRA 2018 49 and project “Dinamica di equazioni nonlineari dispersive”, “Fon-dazione di Sardegna”, 2016. T. O. was supported by Grant-in-Aid for Scientific Research (A) Number 26247014. The authors would like to thank the referee for his/her helpful suggestions to improve a preliminary version of the paper. Publisher Copyright: {\textcopyright} 2019 American Institute of Mathematical Sciences. All Rights Reserved.",
year = "2019",
month = may,
doi = "10.3934/dcds.2019111",
language = "English",
volume = "39",
pages = "2661--2678",
journal = "Discrete and Continuous Dynamical Systems- Series A",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
}