Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 1
125
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Global existence of weak solutions for the 3D incompressible Keller–Segel–Navier–Stokes equations with partial diffusion

, &
Pages 353-376 | Received 27 May 2022, Accepted 09 Feb 2023, Published online: 11 Mar 2023

References

  • Kiselev A, Ryzhik L. Biomixing by chemotaxis and enhancement of biological reactions. Commun Partial Differ Equ. 2012;37(2):298–318.
  • Kiselev A, Ryzhik L. Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case. J Math Phys. 2012;53:Article ID 115609.
  • Coll JC, et al. Chemical aspects of mass spawning in corals. I. Sperm-attractant molecules in the eggs of the scleractinian coral Montipora digitata. Mar Biol. 1994;118(2):177–182.
  • Coll JC, et al. Chemical aspects of mass spawning in corals. II. (-)-Epi-thunbergol, the sperm attractant in the eggs of the soft coral Lobophytum crassum (Cnidaria:Octocorallia). Mar Biol. 1995;123(1):137–143.
  • Miller RL. Sperm chemotaxis in hydromedusae. I. Species specificity and sperm behavior. Mar Biol. 1979;53(2):99–113.
  • Miller RL. Demonstration of sperm chemotaxis in Echinodermata: Asteroidea, Holothuroidea, Ophiuroidea. J Exp Zool. 1985;234:383–414.
  • Ahn J, Kang K, Kim J, et al. Lower bound of mass in a chemotactic model with advection and absorbing reaction. SIAM J Math Anal. 2017;49:723–755.
  • Cao X, Winkler M. Sharp decay estimates in a bioconvection model with quadratic degradation in bounded domains. P Roy Soc Edinb A. 2018;148(5):1–17.
  • Keller EF, Segel LA. Initiation of slime mold aggregation viewed as an instability. J Theoret Biol. 1970;26:399–415.
  • Bellomo N, Bellouquid A, Tao Y, et al. Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Math Models Methods Appl Sci. 2015;25:1663–1763.
  • Winkler M. Boundedness in the higher-dimensional parabolic-parabolic chemotaxis system with logistic source. Commun Partial Differ Equ. 2010;35(8):1516–1537.
  • Winkler M. Aggregation vs global diffusive behavior in the higher-dimensional Keller-Segel model. J Differ Equ. 2010;248:2889–2905.
  • Winkler M. Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system. J Math Pures Appl. 2013;100:748–767.
  • Tao Y, Winkler M. Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system. Z Angew Math Phys. 2016;67:138.
  • Tao Y, Winkler M. Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system. Z Angew Math Phys. 2015;66:2555–2573.
  • Winkler M. Reaction-driven relaxation in three-dimensional Keller-Segel-Navier-Stokes interaction. Commun Math Phys. 2022;389:439–489.
  • Jin C. Large time periodic solutions to coupled chemotaxis-fluid models. Z Angew Math Phys. 2017;68:137.
  • Zhang Q, Zhang Y. On the global well-posedness for the 2D incompressible Keller-Segel- Navier-Stokes equations. Z Angew Math Mech. 2019;99(11):e201900024.
  • Zhang Q, Zhang Y. Global well-posedness for the 3D incompressible Keller-Segel-Navier-Stokes equations. Z Angew Math Phys. 2019;70:140.
  • Hua Q, Zhang Q. On the global well-posedness for the 3D axisymmetric incompressible Keller-Segel-Navier-Stokes equations. Z Angew Math Phys. 2021;72:179.
  • Di Francesco M, Lorz A, Markowich P. Chemotaxis fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior. Discrete Contin Dyn Syst. 2010;28:1437–1453.
  • Liu JG, Lorz A. A coupled chemotaxis-fluid model: global existence. Ann Inst H Poincaré Anal Non Linéare. 2011;28:643–652.
  • Lorz A. A coupled Keller-Segel-Stokes model: global existence for small initial data and blow-up delay. Commun Math Sci. 2012;10:555–574.
  • Meng L, Yuan J, Zheng X. Global existence of almost energy solution to the two-dimensional chemotaxis-Navier-Stokes equations with partial diffusion. Discrete Contin Dyn Syst. 2019;39(6):3413–3441.
  • Tao Y, Winkler M. Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion. Discrete Contin Dyn Syst. 2012;32:1901–1914.
  • Winkler M. Global large-data solutions in a Chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Commun 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 Anal Non Linéaire. 2016;33:1329–1352.
  • Zhang Q, Zheng X. Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations. SIAM J Math Anal. 2014;46:3078–3105.
  • Zhang Q, Wang P. Global well-posedness for the 2D incompressible four-component chemotaxis-Navier-Stokes equations. J Differ Equ. 2020;269:1656–1692.
  • Zhang Q, Zheng X. Global well-posedness of axisymmetric solution to the 3D axisymmetric chemotaxis-Navier-Stokes equations with logistic source. J Differ Equ. 2021;274:576–612.
  • Zhao J, Chen X, Zhang Q. Global existence of weak solutions for the 2D incompressible Keller-Segel-Navier-Stokes equations with partial diffusion. Acta Appl Math. 2022;181:8.
  • Miao C, Wu J, Zhang Z. Littlewood-Paley theory and applications to fluid dynamics equations. In: Monogr. Modern Pure Math., vol. 142. Beijing: Science Press; 2012.
  • Majda A. Vorticity and incompressible flow. Cambridge: Cambridge University Press; 2002. (Cambridge Texts Appl. Math.; vol. 27).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.