Details
| Original language | English |
|---|---|
| Pages (from-to) | 2071-2109 |
| Number of pages | 39 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 26 |
| Issue number | 11 |
| Publication status | Published - 30 Sept 2016 |
| Externally published | Yes |
Abstract
We consider the coupled chemotaxis Navier-Stokes model with logistic source terms:{equation presented} in a bounded, smooth domain Ω?3 under homogeneous Neumann boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u and with given functions fϵ L∞(Ω× (0,∞)) satisfying certain decay conditions and φC1+β(Ω) for some βϵ (0, 1). We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state (K/μ, 0, 0).
Keywords
- boundedness, Chemotaxis, large-time behaviour, logistic source, Navier-Stokes
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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In: Mathematical Models and Methods in Applied Sciences, Vol. 26, No. 11, 30.09.2016, p. 2071-2109.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Long-term behaviour in a chemotaxis-fluid system with logistic source
AU - Lankeit, Johannes
PY - 2016/9/30
Y1 - 2016/9/30
N2 - We consider the coupled chemotaxis Navier-Stokes model with logistic source terms:{equation presented} in a bounded, smooth domain Ω?3 under homogeneous Neumann boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u and with given functions fϵ L∞(Ω× (0,∞)) satisfying certain decay conditions and φC1+β(Ω) for some βϵ (0, 1). We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state (K/μ, 0, 0).
AB - We consider the coupled chemotaxis Navier-Stokes model with logistic source terms:{equation presented} in a bounded, smooth domain Ω?3 under homogeneous Neumann boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u and with given functions fϵ L∞(Ω× (0,∞)) satisfying certain decay conditions and φC1+β(Ω) for some βϵ (0, 1). We construct weak solutions and prove that after some waiting time they become smooth and finally converge to the semi-trivial steady state (K/μ, 0, 0).
KW - boundedness
KW - Chemotaxis
KW - large-time behaviour
KW - logistic source
KW - Navier-Stokes
UR - http://www.scopus.com/inward/record.url?scp=84990235287&partnerID=8YFLogxK
U2 - 10.1142/S021820251640008X
DO - 10.1142/S021820251640008X
M3 - Article
AN - SCOPUS:84990235287
VL - 26
SP - 2071
EP - 2109
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 11
ER -