| Title:
|
Uniqueness of weak solutions to a Keller-Segel-Navier-Stokes model with a logistic source (English) |
| Author:
|
Chen, Miaochao |
| Author:
|
Lu, Shengqi |
| Author:
|
Liu, Qilin |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
67 |
| Issue:
|
1 |
| Year:
|
2022 |
| Pages:
|
93-101 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Keller-Segel-Navier-Stokes system |
| Keyword:
|
uniqueness |
| Keyword:
|
weak solution |
| MSC:
|
22E46 |
| MSC:
|
35Q30 |
| MSC:
|
53C35 |
| MSC:
|
57S20 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 07478519 |
| idMR:
|
MR4392407 |
| DOI:
|
10.21136/AM.2021.0069-20 |
| . |
| Date available:
|
2022-02-08T10:50:08Z |
| Last updated:
|
2024-03-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149361 |
| . |
| Reference:
|
[1] Biler, P.: Global solutions to some parabolic-elliptic systems of chemotaxis.Adv. Math. Sci. Appl. 9 (1999), 347-359. Zbl 0941.35009, MR 1690388 |
| Reference:
|
[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. Zbl 1115.35136, MR 2099126, 10.1007/s00032-003-0026-x |
| Reference:
|
[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. MR 4120539, 10.4310/CMS.2020.v18.n3.a10 |
| Reference:
|
[4] Fan, J., Li, F.: Global strong solutions to a coupled chemotaxis-fluid model with subcritical sensitivity.Acta Appl. Math. 169 (2020), 767-791. MR 4146923, 10.1007/s10440-020-00321-1 |
| Reference:
|
[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. Zbl 1406.35271, MR 3927584, 10.3934/dcdsb.2018119 |
| Reference:
|
[6] Hillen, T., Painter, K. J.: A user's guide to PDE models for chemotaxis.J. Math. Biol. 58 (2009), 183-217. Zbl 1161.92003, MR 2448428, 10.1007/s00285-008-0201-3 |
| Reference:
|
[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. Zbl 1071.35001, MR 2013508 |
| Reference:
|
[8] Keller, E. F., Segel, L. A.: Initiation of slime mold aggregation viewed as an instability.J. Theor. Biol. 26 (1970), 399-415. Zbl 1170.92306, MR 3925816, 10.1016/0022-5193(70)90092-5 |
| Reference:
|
[9] Keller, E. F., Segel, L. A.: Model for chemotaxis.J. Theor. Biol. 30 (1971), 225-234. Zbl 1170.92307, 10.1016/0022-5193(71)90050-6 |
| Reference:
|
[10] Keller, E. F., Segel, L. A.: Traveling bands of chemotactic bacteria: A theoretical analysis.J. Theor. Biol. 30 (1971), 235-248. Zbl 1170.92308, 10.1016/0022-5193(71)90051-8 |
| Reference:
|
[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. Zbl 1343.35069, MR 3452713, 10.1016/j.jfa.2015.10.016 |
| Reference:
|
[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. Zbl 1055.35087, MR 1980623, 10.1007/s002090100332 |
| Reference:
|
[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). Zbl 0645.46031, MR 0785568 |
| Reference:
|
[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. Zbl 1083.35096, MR 2028918, 10.2748/tmj/1113246381 |
| Reference:
|
[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. Zbl 1073.35118, MR 2136032, 10.1137/S0036139902415117 |
| Reference:
|
[16] Winkler, M.: Global solutions in a fully parabolic chemotaxis system with singular sensitivity.Math. Methods Appl. Sci. 34 (2011), 176-190. Zbl 1291.92018, MR 2778870, 10.1002/mma.1346 |
| Reference:
|
[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. Zbl 1408.35132, MR 3912779, 10.1016/j.jfa.2018.12.009 |
| Reference:
|
[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. Zbl 1104.35007, MR 2218162, 10.1017/S0308210500004649 |
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