TY - JOUR
T1 - COUPLED CHEMOTAXIS FLUID MODEL
AU - LORZ, ALEXANDER
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). A. L. would like to thank Peter Markowich, Adrien Blanchet and Klemens Fellner for useful discussions, Prof. Ray Goldstein and the Goldstein Lab. at DAMTP for ongoing and invaluable discussions as well as for permission to use the pictures. Moreover, A. L. would like to kindly thank the referee for his highly useful comments in order to improve this paper.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/4/26
Y1 - 2012/4/26
N2 - We consider a model system for the collective behavior of oxygen-driven swimming bacteria in an aquatic fluid. In certain parameter regimes, such suspensions of bacteria feature large-scale convection patterns as a result of the hydrodynamic interaction between bacteria. The presented model consist of a parabolicparabolic chemotaxis system for the oxygen concentration and the bacteria density coupled to an incompressible Stokes equation for the fluid driven by a gravitational force of the heavier bacteria. We show local existence of weak solutions in a bounded domain in d, d = 2, 3 with no-flux boundary condition and in 2 in the case of inhomogeneous Dirichlet conditions for the oxygen. © 2010 World Scientific Publishing Company.
AB - We consider a model system for the collective behavior of oxygen-driven swimming bacteria in an aquatic fluid. In certain parameter regimes, such suspensions of bacteria feature large-scale convection patterns as a result of the hydrodynamic interaction between bacteria. The presented model consist of a parabolicparabolic chemotaxis system for the oxygen concentration and the bacteria density coupled to an incompressible Stokes equation for the fluid driven by a gravitational force of the heavier bacteria. We show local existence of weak solutions in a bounded domain in d, d = 2, 3 with no-flux boundary condition and in 2 in the case of inhomogeneous Dirichlet conditions for the oxygen. © 2010 World Scientific Publishing Company.
UR - http://hdl.handle.net/10754/597889
UR - https://www.worldscientific.com/doi/abs/10.1142/S0218202510004507
UR - http://www.scopus.com/inward/record.url?scp=77954329528&partnerID=8YFLogxK
U2 - 10.1142/S0218202510004507
DO - 10.1142/S0218202510004507
M3 - Article
SN - 0218-2025
VL - 20
SP - 987
EP - 1004
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 06
ER -