Global existence and asymptotic stability of the fractional chemotaxis–fluid system in R3. (June 2019)

• Record Type: Journal Article
• Authors: Zhu, Shanshan; Liu, Zuhan; Zhou, Ling
• Is Part Of: Nonlinear analysis. Volume 183(2019)
• Page Start: 149
• Page End: 190
• Publication Date: 2019-06
• Subjects: 35A01 -- 35Q30 -- 35Q35; Fractional chemotaxis system -- Navier–Stokes equations -- Negative Sobolev space -- Asymptotic stability; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider a model arising from biology, consisting of fractional chemotaxis equations coupled to viscous incompressible fluid equations throughout transport and external force in R 3 . We establish the existence and uniqueness of global solution with small initial data by combining the local existence and a priori estimates as well as continuation argument. Moreover, the decay rates of the solutions and their higher-order spatial derivatives are established towards the equilibrium by introducing the negative Sobolev space H ̇ − s ( 0 ⩽ s < 3 2 ).