In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. The global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the Chemotaxis-Navier-Stokes system over three space dimensions, we obtain global existence and rates of convergence on classical solutions near constant states. When the fluid motion is described by the simpler Stokes equations, we prove global existence of weak solutions in two space dimensions for cell density with finite mass, first-order spatial moment and entropy provided that the external forcing is weak or the substrate concentration is small. © Taylor & Francis Group, LLC.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: This research is supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST). R.-J. Duan would like to thank RICAM for its support during the postdoctoral studies of the year 2008-09. A. Lorz would like to acknowledge support by KAUST. P. Markowich acknowledges support from his Royal Society Wolfson Research Merit Award. The authors would like to thank the anonymous referees for their valuable comments which improved the current results so much.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.