On the global existence of weak solutions for the Cucker-Smale-Navier-Stokes system with shear thickening
- Authors
- Ha, Seung-Yeal; Kim, Hwa Kil; Kim, Jae-Myoung; Park, Jinyeong
- Issue Date
- Nov-2018
- Publisher
- SCIENCE PRESS
- Keywords
- emergence; flocking; Cucker-Smale model; Navier-Stokes equation; non-Newtonian fluid
- Citation
- SCIENCE CHINA-MATHEMATICS, v.61, no.11, pp.2033 - 2052
- Indexed
- SCIE
SCOPUS
- Journal Title
- SCIENCE CHINA-MATHEMATICS
- Volume
- 61
- Number
- 11
- Start Page
- 2033
- End Page
- 2052
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/149039
- DOI
- 10.1007/s11425-017-9301-y
- ISSN
- 1674-7283
- Abstract
- We study the large-time dynamics of Cucker-Smale (C-S) flocking particles interacting with non-Newtonian incompressible fluids. Dynamics of particles and fluids were modeled using the kinetic Cucker-Smale equation for particles and non-Newtonian Navier-Stokes system for fluids, respectively and these two systems are coupled via the drag force, which is the main flocking (alignment) mechanism between particles and fluids. We present a global existence theory for weak solutions to the coupled Cucker-Smale-Navier-Stokes system with shear thickening. We also use a Lyapunov functional approach to show that sufficiently regular solutions approach flocking states exponentially fast in time.
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