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Hou, Qianqian

Chemical diffusion limit of a chemotaxis-Navier-Stokes system. (English) Zbl 1541.35022

Appl. Anal. 103, No. 1, 198-210 (2024).

MSC:

35B25 Singular perturbations in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
35K59 Quasilinear parabolic equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences

Keywords:

chemotaxis-Navier-Stokes; vanishing diffusion limit; convergence rate
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Full Text: DOI

References:

[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.
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