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Time periodic solutions for a two-species chemotaxis-Navier-Stokes system
Department of Mathematics, Jilin University, Changchun 130012, China |
We consider a chemotaxis-Navier-Stokes system in two dimensional bounded domains. It is asserted that the chemotaxis system admits a time periodic solution under some conditions.
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X. Cao,
Global classical solutions in chemotaxis-Navier-Stokes system with rotational flux term, J. Differential Equations, 261 (2016), 6883-6914.
doi: 10.1016/j.jde.2016.09.007. |
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X. Cao, S. Kurima and M. Mizukami,
Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics, Math. Meth. Appl. Sci., 41 (2018), 3138-3154.
doi: 10.1002/mma.4807. |
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C. Jin, Large time periodic solutions to coupled chemotaxis-fluid models, Z. Angew. Math. Phys., 68 (2017), 24 pp.
doi: 10.1007/s00033-017-0882-9. |
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C. Jin,
Large time periodic solution to the coupled chemotaxis-Stokes model, Math. Nachr., 290 (2017), 1701-1715.
doi: 10.1002/mana.201600180. |
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H. Jin and T. Xiang,
Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes system with competitive kinetics, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 1919-1942.
doi: 10.3934/dcdsb.2018249. |
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R. Farwig and T. Okabe,
Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56 (2010), 249-281.
doi: 10.1007/s11565-010-0108-y. |
| [7] |
J. Liu, Boundedness in a Chemotaxis-Navier-Stokes system modeling coral fertilization with slow p-Laplacian diffusion, J. Math. Fluid Mech., 22 (2020), 31 pp.
doi: 10.1007/s00021-019-0469-7. |
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W. Tao and Y. Li,
Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with slow p-Laplacian diffusion, Nonlinear Anal. Real World Appl., 45 (2019), 26-52.
doi: 10.1016/j.nonrwa.2018.06.005. |
| [9] |
W. Tao and Y. Li,
Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion, J. Differential Equations, 268 (2020), 6872-6919.
doi: 10.1016/j.jde.2019.11.078. |
| [10] |
I. Tuval, L. Cisneros, C. Dombrowski, C. Wolgemuth, J. Kessler and R. Goldstein,
Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. USA, 102 (2005), 2277-2282.
doi: 10.1073/pnas.0406724102. |
| [11] |
Y. Wang, M. Winkler and Z. Xiang,
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 18 (2018), 421-466.
doi: 10.2422/2036-2145.201603_004. |
| [12] |
M. Winkler,
Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 33 (2016), 1329-1352.
doi: 10.1016/j.anihpc.2015.05.002. |
| [13] |
M. Winkler,
Global large-data solutions in a chemotaxis-Navier-Stokes system modeling cellular swimming in fluid drops, Comm. Partial Differential Equations, 37 (2012), 319-351.
doi: 10.1080/03605302.2011.591865. |
| [14] |
M. Winkler,
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?, Trans. Amer. Math. Soc., 369 (2017), 3067-3125.
doi: 10.1090/tran/6733. |
| [15] |
Q. Zhang and Y. Li,
Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 2751-2759.
doi: 10.3934/dcdsb.2015.20.2751. |
| [16] |
Q. Zhang and X. Zheng,
Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations, SIAM J. Math. Anal., 46 (2014), 3078-3105.
doi: 10.1137/130936920. |
show all references
References:
| [1] |
X. Cao,
Global classical solutions in chemotaxis-Navier-Stokes system with rotational flux term, J. Differential Equations, 261 (2016), 6883-6914.
doi: 10.1016/j.jde.2016.09.007. |
| [2] |
X. Cao, S. Kurima and M. Mizukami,
Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics, Math. Meth. Appl. Sci., 41 (2018), 3138-3154.
doi: 10.1002/mma.4807. |
| [3] |
C. Jin, Large time periodic solutions to coupled chemotaxis-fluid models, Z. Angew. Math. Phys., 68 (2017), 24 pp.
doi: 10.1007/s00033-017-0882-9. |
| [4] |
C. Jin,
Large time periodic solution to the coupled chemotaxis-Stokes model, Math. Nachr., 290 (2017), 1701-1715.
doi: 10.1002/mana.201600180. |
| [5] |
H. Jin and T. Xiang,
Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes system with competitive kinetics, Discrete Contin. Dyn. Syst. Ser. B, 24 (2019), 1919-1942.
doi: 10.3934/dcdsb.2018249. |
| [6] |
R. Farwig and T. Okabe,
Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56 (2010), 249-281.
doi: 10.1007/s11565-010-0108-y. |
| [7] |
J. Liu, Boundedness in a Chemotaxis-Navier-Stokes system modeling coral fertilization with slow p-Laplacian diffusion, J. Math. Fluid Mech., 22 (2020), 31 pp.
doi: 10.1007/s00021-019-0469-7. |
| [8] |
W. Tao and Y. Li,
Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with slow p-Laplacian diffusion, Nonlinear Anal. Real World Appl., 45 (2019), 26-52.
doi: 10.1016/j.nonrwa.2018.06.005. |
| [9] |
W. Tao and Y. Li,
Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion, J. Differential Equations, 268 (2020), 6872-6919.
doi: 10.1016/j.jde.2019.11.078. |
| [10] |
I. Tuval, L. Cisneros, C. Dombrowski, C. Wolgemuth, J. Kessler and R. Goldstein,
Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. USA, 102 (2005), 2277-2282.
doi: 10.1073/pnas.0406724102. |
| [11] |
Y. Wang, M. Winkler and Z. Xiang,
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 18 (2018), 421-466.
doi: 10.2422/2036-2145.201603_004. |
| [12] |
M. Winkler,
Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 33 (2016), 1329-1352.
doi: 10.1016/j.anihpc.2015.05.002. |
| [13] |
M. Winkler,
Global large-data solutions in a chemotaxis-Navier-Stokes system modeling cellular swimming in fluid drops, Comm. Partial Differential Equations, 37 (2012), 319-351.
doi: 10.1080/03605302.2011.591865. |
| [14] |
M. Winkler,
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?, Trans. Amer. Math. Soc., 369 (2017), 3067-3125.
doi: 10.1090/tran/6733. |
| [15] |
Q. Zhang and Y. Li,
Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 2751-2759.
doi: 10.3934/dcdsb.2015.20.2751. |
| [16] |
Q. Zhang and X. Zheng,
Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations, SIAM J. Math. Anal., 46 (2014), 3078-3105.
doi: 10.1137/130936920. |
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