References
- Tuval I, Cisneros L, Dombrowski C, et al. Bacterial swimming and oxygen transport near contact lines. Proc Natl Acad Sci. 2005;102:2277–2282.
- Lorz A. Coupled chemotaxis fluid equations. Math Models Methods Appl Sci. 2010;20:987–1004.
- Winkler M. Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Comm Partial Differ Equ. 2012;37:319–351.
- Winkler M. Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Arch Ration Mech Anal. 2014;211:455–487.
- Winkler M. Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Ann Inst H Poincaré C Anal Non Linéaire. 2016;33:1329–1352.
- Winkler M. How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Trans Amer Math Soc. 2017;369:3067–3125.
- Zhang Q, Li Y. Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system. Discrete Contin Dyn Syst B. 2015;20:2751–2759.
- Peng Y, Xiang Z. Global solutions to the coupled chemotaxis-fluids system in a 3D unbounded domain with boundary. Math Models Methods Appl Sci. 2018;28:869–920.
- Braukhoff M. Global (weak) solution of the chemotaxis-Navier-Stokes equations with non-homogeneous boundary conditions and logistic growth. Ann Inst H Poincaré C Anal Non Linéaire. 2017;34:1013–1039.
- Braukhoff M, Lankeit J. Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions for the oxygen. Math Models Methods Appl Sci. 2019;29:2033–2062.
- Braukhoff M, Tang BQ. Global solutions for chemotaxis-Navier-Stokes system with robin boundary conditions. J Differ Equ. 2020;269:10630–10669.
- Fuest M, Lankeit J, Mizukami M. Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model. J Differ Equ. 2021;271:254–279.
- Peng YP, Xiang ZY. Global existence and convergence rates to a chemotaxis-fluids system with mixed boundary conditions. J Differ Equ. 2019;267:1277–1321.
- Wang YL, Winkler M, Xiang ZY. Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary. Comm Partial Differ Equ. 2021;46:1058–1091.
- Ke Y, Zheng J. An optimal result for global existence in a three-dimensional Keller-Segel-Navier-Stokes system involving tensor-valued sensitivity with saturation. Calc Var Partial Differ Equ. 2019;58:1–27.
- Winkler M. Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotation flux components. J Evol Eqns. 2018;18:1267–1289.
- Zheng J. An optimal result for global existence and boundedness in a three-dimensional Keller-Segel-Stokes system with nonlinear diffusion. J Differ Equ. 2019;267:2385–2415.
- Zheng J. A new result for the global existence (and boundedness) and regularity of a three-dimensional Keller-Segel-Navier-Stokes system modeling coral fertilization. J Differ Equ. 2021;272:164–202.
- Zheng J. Eventual smoothness and stabilization in a three-dimensional Keller-Segel-Navier-Stokes system with rotational flux. Calc Var Partial Differ Equ. 2022;61:52.
- Duan R, Lorz A, Markowich P. Global solutions to the coupled chemotaxis-fluid equations. Comm Partial Differ Equ. 2010;35:1635–1673.
- Liu J, Lorz A. A coupled chemotaxis-fluid model: global existence. Ann Inst H Poincaré C Anal Non Linéaire. 2011;28:643–652.
- Zhang Q, Zheng X. Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations. SIAM J Math Anal. 2014;46:3078–3105.
- Chae M, Kang K, Lee J. Existence of smooth solutions to coupled chemotaxis-fluid equations. Discrete Contin Dyn Syst A. 2013;33:2271–2297.
- Chae M, Kang K, Lee J. Global existence and temporal decay in Keller-Segel models coupled to fluid equations. Comm Partial Differ Equ. 2014;39:1205–1235.
- Constantin P. Note on loss of regularity for solutions of the 3d incompressible Euler and related equations. Comm Math Phys. 1986;104:311–326.
- Hou QQ. Global well-posedness and boundary layer effects of radially symmetric solutions for the singular Keller-Segel model. J Math Fluid Mech. 2022;24:24.
- Adams RA, Fournier JJF. Sobolev spaces. Singapore: Elsevier Pte Ltd; 2009.