@article{Gu2023, 
author = {Caihong Gu and Yanbin Tang},
title = {Global solution to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {1},
pages = {109-139},
keywords = {Drift-diffusion system, Keller-Segel equations, global solutions, fractional Laplacian, asymptotic behavior, multi-linear operator},
url = {https://www.sciopen.com/article/10.3934/nhm.2023005},
doi = {10.3934/nhm.2023005},
abstract = {In this paper, we consider the global existence, regularizing decay rate and asymptotic behavior of mild solutions to Cauchy problem of fractional drift diffusion system with power-law nonlinearity. Using the properties of fractional heat semigroup and the classical estimates of fractional heat kernel, we first prove the global-in-time existence and uniqueness of the mild solutions in the frame of mixed time-space Besov space with multi-linear continuous mappings. Then, we show the asymptotic behavior and regularizing-decay rate estimates of the solution to equations with power-law nonlinearity by the method of multi-linear operator and the classical Hardy-Littlewood-Sobolev inequality.}
}