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. A 33 2271-97) and Chae et al (2014 Commun.
Bibliographical noteFunding Information:
M Chae was supported by NRF-2015R1C1A2A01054919. K Kang was supported by NRF-2014R1A2A1A11051161. J Lee was supported by NRF-2016R1A2B3011647. Ki-Ahm Lee was supported by NRF-2015R1A4A1041675. Ki-Ahm Lee also hold a joint appointment with the Research Institute of Mathematics of Seoul National University.
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics