References
- Keller EF, Segel LA. Initiation of slime mold aggregation viewed as an instability. J Theoret Biol. 1970;26:399–415. doi: https://doi.org/10.1016/0022-5193(70)90092-5
- Mimura M, Tsujikawa T. Aggregating pattern dynamics in a chemitaxis model including growth. Physica A. 1996;230(3–4):499–543. doi: https://doi.org/10.1016/0378-4371(96)00051-9
- Winkler M. Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Comm Partial Differ Equ. 2010;35:1516–1537. doi: https://doi.org/10.1080/03605300903473426
- Painter KJ, Hillen T. Volume-filling and quorum-sensing in models for chemosensitive movement. Can Appl Math Quart. 2002;10:501–543.
- Henry M, Hilhorst D, Schätzle R. Convergence to a viscocity solution for an advection-reaction-diffusion equation arising from a chemotaxis-growth model. Hiroshima Math J. 1999;29:591–630. doi: https://doi.org/10.32917/hmj/1206124856
- Lorz A. Coupled chemotaxis fluid model. Math Models Methods Appl Sci. 2010;20:987–1004. doi: https://doi.org/10.1142/S0218202510004507
- Tuval I, Cisneros L, Dombrowski C, et al. Bacterial swimming and oxygen transport near constant lines. Proc Natl Acad Sci USA. 2005;102:2277–2282. doi: https://doi.org/10.1073/pnas.0406724102
- Liu JG, Lorz A. A coupled chemotaxis-fluid model: global existence. Ann Inst H.Poincaré Anal Non Linéaire. 2011;28:643–652. doi: https://doi.org/10.1016/j.anihpc.2011.04.005
- Winkler M. Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Comm Partial Differ Equ. 2012;37:319–352. doi: https://doi.org/10.1080/03605302.2011.591865
- Zhang Q, Zheng X. Global well-posedness for the two-dimensional incompressible chemptaxis-Navier-Stokes equations. SIAM J Math Anal. 2014;46:3078–3105. doi: https://doi.org/10.1137/130936920
- Winkler M. Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. J Math Pures Appl. 2013;100:748–767. doi: https://doi.org/10.1016/j.matpur.2013.01.020
- Zhang Q, Li Y. Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system. Discrete Contin Dynam Syst Ser B. 2015;20:2751–2759. doi: https://doi.org/10.3934/dcdsb.2015.20.2751
- Duan RJ, Lorz A, Markowich PA. Global solutions to the coupled chemotaxis-fluid equations. Comm Partial Differ Equ. 2010;35:1635–1673. doi: https://doi.org/10.1080/03605302.2010.497199
- Winkler M. Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Ann Inst H Poincaré Anal Non Linéaire. 2016;33:1329–1352. doi: https://doi.org/10.1016/j.anihpc.2015.05.002
- Winkler M. How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?Trans Amer Math Soc. 2017;369:3067–3125. doi: https://doi.org/10.1090/tran/6733
- He H, Zhang Q. Global existence of weak solutions for the 3D chemotaxis-Navier-Stokes equations. Nonlinear Anal Real World Appl. 2017;35:336–349. doi: https://doi.org/10.1016/j.nonrwa.2016.11.006
- Chertock A, Fellner K, Kurganov A, et al. Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach. J Fluid Mech. 2012;694:155–190. doi: https://doi.org/10.1017/jfm.2011.534
- Lorz A. A coupled Keller-Segel-Stokes model: global existence for small initial data and blowup delay. Commun Math Sci. 2012;10:555–574. doi: https://doi.org/10.4310/CMS.2012.v10.n2.a7
- Tao Y, Winkler M. Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Discrete Contin Dynam Syst. 2012;32:1901–1914. doi: https://doi.org/10.3934/dcds.2012.32.1901
- Tao Y, Winkler M. Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Ann Inst H Poincaré Anal Non Linéaire. 2013;30:157–178. doi: https://doi.org/10.1016/j.anihpc.2012.07.002
- Tao Y, Winkler M. Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion. Ann Inst H Poincaré Anal Non Linéaire. 2013;30:157–178. doi: https://doi.org/10.1016/j.anihpc.2012.07.002
- Zhang Q, Li Y. Global weak solutions for the three-dimensional chemotaxis- Navier-Stokes system with nonlinear diffusion. J Differ Equ. 2015;259:3730–3754. doi: https://doi.org/10.1016/j.jde.2015.05.012
- Cao X, Lankeit J. Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities. Calc Var Partial Differ Equ. 2016;55:1–39. doi: https://doi.org/10.1007/s00526-016-1027-2
- Wang Y, Cao X. Global classical solutions of a 3D chemotaxis-Stokes system with rotation. Discrete Contin Dynam Syst Ser B. 2015;204:3235–3254.
- Wang Y, Xiang Z. Global existence and boundedness in a Keller–Segel–Stokes system involving a tensor-valued sensitivity with saturation. J Differ Equ. 2015;259:7578–7609. doi: https://doi.org/10.1016/j.jde.2015.08.027
- Lankeit J. Long-term behaviour in a chemotaxis-fluid system with logistic source. Math Models Methods Appl Sci. 2016;26(11):2071–2109. doi: https://doi.org/10.1142/S021820251640008X
- Bahouri H, Chemin JY, Danchin R. Fourier analysis and nonlinear partial differential equations. Berlin: Springer-Verlag; 2011.
- Miao C, Wu J, Zhang Z. Littlewood-Paley theory and applications to fluid dynamics equations. Beijing: Science Press; 2012. (Monographs on modern pure mathematics; Vol. 142).
- Majda A, Bertozzi AL. Vorticity and incompressible flow. Cambridge: Cambridge University Press; 2002.