Publication Cover
Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 7
298
Views
3
CrossRef citations to date
0
Altmetric
Articles

A note on the global existence of a two-dimensional chemotaxis-Navier–Stokes system

&
Pages 1224-1235 | Received 31 Jul 2017, Accepted 11 Dec 2017, Published online: 28 Dec 2017

References

  • Tuval I , Cisneros L , Dombrowski C , et al . Bacterial swimming and oxygen transport near contact lines. PNAS. 2005;102:2277–2282.
  • 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.
  • Chae M , Kang K , Lee J . On existence of the smooth solutions to the coupled chemotaxis-fluid equations. Discrete Cont Dyn Syst A. 2013;33:2271–2297.
  • Chae M , Kang K , Lee J . Global existence and temporal decay in Keller-Segel models coupled to fluid equations. Commun Partial Differ Equ. 2014;39:1205–1235.
  • Duan R , Lorz A , Markowich P . Global solutions to the coupled chemotaxis-fluid equations. Commun Partial Differ Equ. 2010;35:1635–1673.
  • Duan R , Xiang Z . A note on global existence for the chemotaxis Stokes model with nonlinear diffusion. Int Math Res Notices. 2014;2014:1833–1852.
  • 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 Funct Anal. 2016;270:1663–1683.
  • Lankeit J . Long-term behaviour in a chemotaxis-fluid system with logistic source. Math Models Methods Appl Sci. 2016;26:2071–2109.
  • Liu J-G , Lorz A . A coupled chemotaxis-fluid model. Ann Inst H Poincaré Anal Non Linéaire. 2011;28:643–652.
  • Wang Y , Winkler M , Xiang Z . The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system. Math Z. 2018. DOI:10.1007/s00209-017-1944-6
  • Winkler M . Global large-date solutions in a chemotaxis-Navier-Stokes system modeling cellular swimming in fluid crops. 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.
  • Winkler M . How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? Trans Amer Math Soc. 2017;369:3067–3125.
  • Petroff A , Libchaber A . Hydrodynamics and collective behavior of the tethered bacterium Thiovulum majus. PNAS. 2014;111:E537–E545.
  • Duan R , Li X , Xiang Z . Global existence and large time behavior for a two dimensional chemotaxis-Navier-Stokes system. J Differ Equ. 2017;263:6284–6316.
  • Cao X , Lankeit J . Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities. Calc Var. 2016;55:107.
  • Li X , Wang Y , Xiang Z . Global existence and boundedness in a 2D Keller-Segel-Stokes system with nonlinear diffusion and rotational flux. Commun Math Sci. 2016;14:1889–1910.
  • Peng Y , Xiang Z . Global existence and boundedness in a 3D Keller-Segel-Stokes system with nonlinear diffusion and rotational flux. Z Angew Math Phys. 2017;68:68.
  • Wang Y . Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system with subcritical sensitivity. Math Models Methods Appl Sci. 2017;27:2745–2780.
  • Wang Y , Winkler M , Xiang Z . Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity. Ann Scuola Norm Sup Pisa Cla Sci (5). 2018;XVIII. DOI:10.2422/2036-2145.201603_004
  • Wang Y , Xiang Z . Global existence and boundedness in a Keller-Segel-Stokes system involving a tensor-valued sensitivity with saturation. J Differ Equ. 2015;259:7578–7609.
  • Wang Y , Xiang Z . Global existence and boundedness in a Keller-Segel-Stokes system involving a tensor-valued sensitivity with saturation: the 3D case. J Differ Equ. 2016;261:4944–4973.
  • Li T , Suen A , Winkler M , et al . Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms. Math Models Methods Appl Sci. 2015;25:721–746.

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.