[1] |
Tuval, I, Cisneros, L, Dombrowski, C, et al. Bacterial swimming and oxygen transport near contact lines. Proc Natl Acad Sci. 2005;102:2277-2282. · Zbl 1277.35332 |
[2] |
Lorz, A.Coupled chemotaxis fluid equations. Math Models Methods Appl Sci. 2010;20:987-1004. · Zbl 1191.92004 |
[3] |
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. · Zbl 1236.35192 |
[4] |
Winkler, M.Stabilization in a two-dimensional chemotaxis-Navier-Stokes system. Arch Ration Mech Anal. 2014;211:455-487. · Zbl 1293.35220 |
[5] |
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. · Zbl 1351.35239 |
[6] |
Winkler, M.How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?Trans Amer Math Soc. 2017;369:3067-3125. · Zbl 1356.35071 |
[7] |
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. · Zbl 1334.35104 |
[8] |
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. · Zbl 1391.35206 |
[9] |
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. · Zbl 1417.92028 |
[10] |
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. · Zbl 1425.35196 |
[11] |
Braukhoff, M, Tang, BQ.Global solutions for chemotaxis-Navier-Stokes system with robin boundary conditions. J Differ Equ. 2020;269:10630-10669. · Zbl 1448.35514 |
[12] |
Fuest, M, Lankeit, J, Mizukami, M.Long-term behaviour in a parabolic-elliptic chemotaxis-consumption model. J Differ Equ. 2021;271:254-279. · Zbl 1455.35267 |
[13] |
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. · Zbl 1412.35174 |
[14] |
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. · Zbl 1470.92044 |
[15] |
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. · Zbl 1412.35172 |
[16] |
Winkler, M.Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotation flux components. J Evol Eqns. 2018;18:1267-1289. · Zbl 1404.35464 |
[17] |
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. · Zbl 1472.35232 |
[18] |
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. · Zbl 1455.35273 |
[19] |
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. · Zbl 1485.35067 |
[20] |
Duan, R, Lorz, A, Markowich, P.Global solutions to the coupled chemotaxis-fluid equations. Comm Partial Differ Equ. 2010;35:1635-1673. · Zbl 1275.35005 |
[21] |
Liu, J, Lorz, A.A coupled chemotaxis-fluid model: global existence. Ann Inst H Poincaré C Anal Non Linéaire. 2011;28:643-652. · Zbl 1236.92013 |
[22] |
Zhang, Q, Zheng, X.Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations. SIAM J Math Anal. 2014;46:3078-3105. · Zbl 1444.35011 |
[23] |
Chae, M, Kang, K, Lee, J.Existence of smooth solutions to coupled chemotaxis-fluid equations. Discrete Contin Dyn Syst A. 2013;33:2271-2297. · Zbl 1277.35276 |
[24] |
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. · Zbl 1304.35481 |
[25] |
Constantin, P.Note on loss of regularity for solutions of the 3d incompressible Euler and related equations. Comm Math Phys. 1986;104:311-326. · Zbl 0655.76041 |
[26] |
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. · Zbl 1490.35026 |
[27] |
Adams, RA, Fournier, JJF.Sobolev spaces. Singapore: Elsevier Pte Ltd; 2009. |