A regularity condition and temporal asymptotics for chemotaxis-fluid equations. (3rd January 2018)

• Record Type: Journal Article
• Authors: Chae, Myeongju; Kang, Kyungkeun; Lee, Jihoon; Lee, Ki-Ahm
• Is Part Of: Nonlinearity. Volume 31:Number 2(2018:Feb.)
• Page Start: 351
• Page End: 387
• Publication Date: 2018-01-03
• Subjects: Chemotaxis–Navier–Stokes -- global well-posedness -- temporal decay; 35Q30 -- 35Q35 -- 76Dxx -- 76Bxx; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa92ec
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: We consider two dimensional chemotaxis equations coupled to the Navier–Stokes equations. We present a new localized regularity criterion that is localized in a neighborhood at each point. Secondly, we establish temporal decays of the regular solutions under the assumption that the initial mass of biological cell density is sufficiently small. Both results are improvements of previously known results given in Chae et al (2013 Discrete Continuous Dyn. Syst . A33 2271–97) and Chae et al (2014 Commun. PDE 39 1205–35)