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Keywords:
Keller-Segel-Navier-Stokes system; uniqueness; weak solution
Keller-Segel-Navier-Stokes system; uniqueness; weak solution
Summary:
We prove a uniqueness result of weak solutions to the $nD$ $(n\geq 3)$ Cauchy problem of a Keller-Segel-Navier-Stokes system with a logistic term.
References:
[1] Biler, P.: Global solutions to some parabolic-elliptic systems of chemotaxis. Adv. Math. Sci. Appl. 9 (1999), 347-359. MR 1690388 | Zbl 0941.35009
[2] Corrias, L., Perthame, B., Zaag, H.: Global solutions of some chemotaxis and angiogenesis systems in high space dimensions. Milan J. Math. 72 (2004), 1-28. DOI 10.1007/s00032-003-0026-x | MR 2099126 | Zbl 1115.35136
[3] Fan, J., Jing, L., Nakamura, G., Zhao, K.: Qualitative analysis of an integrated chemotaxis-fluid model: Global existence and extensibility criterion. Commun. Math. Sci. 18 (2020), 809-836. DOI 10.4310/CMS.2020.v18.n3.a10 | MR 4120539
[4] Fan, J., Li, F.: Global strong solutions to a coupled chemotaxis-fluid model with subcritical sensitivity. Acta Appl. Math. 169 (2020), 767-791. DOI 10.1007/s10440-020-00321-1 | MR 4146923
[5] Fan, J., Zhao, K.: Improved extensibility criteria and global well-posedness of a coupled chemotaxis-fluid model on bounded domains. Discrete Contin. Dyn. Syst., Ser. B 23 (2018), 3949-3967. DOI 10.3934/dcdsb.2018119 | MR 3927584 | Zbl 1406.35271
[6] Hillen, T., Painter, K. J.: A user's guide to PDE models for chemotaxis. J. Math. Biol. 58 (2009), 183-217. DOI 10.1007/s00285-008-0201-3 | MR 2448428 | Zbl 1161.92003
[7] Horstmann, D.: From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I. Jahresber. Dtsch. Math.-Ver. 105 (2003), 103-165. MR 2013508 | Zbl 1071.35001
[8] Keller, E. F., Segel, L. A.: Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26 (1970), 399-415. DOI 10.1016/0022-5193(70)90092-5 | MR 3925816 | Zbl 1170.92306
[9] Keller, E. F., Segel, L. A.: Model for chemotaxis. J. Theor. Biol. 30 (1971), 225-234. DOI 10.1016/0022-5193(71)90050-6 | Zbl 1170.92307
[10] Keller, E. F., Segel, L. A.: Traveling bands of chemotactic bacteria: A theoretical analysis. J. Theor. Biol. 30 (1971), 235-248. DOI 10.1016/0022-5193(71)90051-8 | Zbl 1170.92308
[11] Kozono, H., Miura, M., Sugiyama, Y.: Existence and uniqueness theorem on mild solutions to the Keller-Segel system coupled with the Navier-Stokes fluid. J. Func. Anal. 270 (2016), 1663-1683. DOI 10.1016/j.jfa.2015.10.016 | MR 3452713 | Zbl 1343.35069
[12] Kozono, H., Ogawa, T., Taniuchi, Y.: The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations. Math. Z. 242 (2002), 251-278. DOI 10.1007/s002090100332 | MR 1980623 | Zbl 1055.35087
[13] Maz'ya, V. G., Shaposhnikova, T. O.: Theory of Multipliers in Spaces of Differentiable Functions. Monographs and Studies in Mathematics 23. Pitman, Bostan (1985). MR 0785568 | Zbl 0645.46031
[14] Ogawa, T., Taniuchi, Y.: The limiting uniqueness criterion by vorticity for Navier-Stokes equations in Besov spaces. Tohoku Math. J., II. Ser. 56 (2004), 65-77. DOI 10.2748/tmj/1113246381 | MR 2028918 | Zbl 1083.35096
[15] Sleeman, B. D., Ward, M. J., Wei, J. C.: The existence and stability of spike patterns in a chemotaxis model. SIAM J. Appl. Math. 65 (2005), 790-817. DOI 10.1137/S0036139902415117 | MR 2136032 | Zbl 1073.35118
[16] Winkler, M.: Global solutions in a fully parabolic chemotaxis system with singular sensitivity. Math. Methods Appl. Sci. 34 (2011), 176-190. DOI 10.1002/mma.1346 | MR 2778870 | Zbl 1291.92018
[17] Winkler, M.: A three-dimensional Keller-Segel-Navier-Stokes system with logistic source: Global weak solutions and asymptotic stablization. J. Funct. Anal. 276 (2019), 1339-1401. DOI 10.1016/j.jfa.2018.12.009 | MR 3912779 | Zbl 1408.35132
[18] Wrzosek, D.: Long-time behaviour of solutions to a chemotaxis model with volume filling-effect. Proc. R. Soc. Edinb., Sect. A, Math. 136 (2006), 431-444. DOI 10.1017/S0308210500004649 | MR 2218162 | Zbl 1104.35007
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