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Local well-posedness for the Zakharov system in dimension $ d = 2, 3 $
Time periodic solution to a two-species chemotaxis-Stokes system with $ p $-Laplacian diffusion
Department of Mathematics, Jilin University, Changchun 130012, China |
In this paper, we consider a two-species chemotaxis-Stokes system with $ p $-Laplacian diffusion in two-dimensional smooth bounded domains. It is proved that the existence of time periodic solution for any $ \frac{15}{7}\leq p<3 $ and any large periodic source $ g_1(x,t) $ and $ g_2(x,t) $.
References:
[1] |
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. |
[2] |
J. Han and C. Liu, Global existence for a two-species chemotaxis-Navier-Stokes system with p-Laplacian, Electron. Res. Arch., http://dx.doi.org/10.3934/era.2021050.
doi: 10.3934/era.2021050. |
[3] |
J. Huang and C. Jin,
Time periodic solution to a coupled chemotaxis-fluid model with porous medium diffusion, Discrete Contin. Dyn. Syst., 40 (2020), 5415-5439.
doi: 10.3934/dcds.2020233. |
[4] |
C. Jin, Large time periodic solutions to coupled chemotaxis-fluid models, Z. Angew. Math. Phys., 68 (2017), 24pp.
doi: 10.1007/s00033-017-0882-9. |
[5] |
C. Jin,
Large time periodic solution to the coupled chemotaxis-Stokes model, Math. Nachr., 290 (2017), 1701-1715.
doi: 10.1002/mana.201600180. |
[6] |
C. Jin,
Periodic pattern formation in the coupled chemotaxis-(Navier-)Stokes system with mixed nonhomogeneous boundary conditions, Proc. Roy. Soc. Edinb. Sect. A, 150 (2020), 3121-3152.
doi: 10.1017/prm.2019.62. |
[7] |
C. Liu and P. Li,
Global existence for a chemotaxis-haptotaxis model with p-Laplacian, Commun. Pure Appl. Anal., 19 (2020), 1399-1419.
doi: 10.3934/cpaa.2020070. |
[8] |
C. Liu and P. Li,
Time periodic solutions for a two-species chemotaxis-Navier-Stokes system, Discret. Contin. Dynam. Syst. Series B., 26 (2021), 4567-4585.
doi: 10.3934/dcdsb.2020303. |
[9] |
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. |
[10] |
N. Mizoguchi and P. Souplet,
Nondegeneracy of blow-up points for the parabolic Keller-Segel system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 851-875.
doi: 10.1016/j.anihpc.2013.07.007. |
[11] |
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. |
[12] |
W. Tao and Y. Li,
Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion, J. Differ. Equ., 268 (2020), 6872-6919.
doi: 10.1016/j.jde.2019.11.078. |
[13] |
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. |
[14] |
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. |
[15] |
M. Winkler,
Global large-data solutions in a chemotaxis-Navier-Stokes system modeling cellular swimming in fluid drops, Commun. Partial Differ. Equ., 37 (2012), 319-351.
doi: 10.1080/03605302.2011.591865. |
[16] |
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. |
[17] |
M. Winkler,
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differ. Equ., 248 (2010), 2889-2905.
doi: 10.1016/j.jde.2010.02.008. |
[18] |
J. Yin and C. Jin,
Periodic solutions of the evolutionary p-Laplacian with nonlinear sources, J. Math. Anal. Appl., 368 (2010), 604-622.
doi: 10.1016/j.jmaa.2010.03.006. |
show all references
References:
[1] |
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. |
[2] |
J. Han and C. Liu, Global existence for a two-species chemotaxis-Navier-Stokes system with p-Laplacian, Electron. Res. Arch., http://dx.doi.org/10.3934/era.2021050.
doi: 10.3934/era.2021050. |
[3] |
J. Huang and C. Jin,
Time periodic solution to a coupled chemotaxis-fluid model with porous medium diffusion, Discrete Contin. Dyn. Syst., 40 (2020), 5415-5439.
doi: 10.3934/dcds.2020233. |
[4] |
C. Jin, Large time periodic solutions to coupled chemotaxis-fluid models, Z. Angew. Math. Phys., 68 (2017), 24pp.
doi: 10.1007/s00033-017-0882-9. |
[5] |
C. Jin,
Large time periodic solution to the coupled chemotaxis-Stokes model, Math. Nachr., 290 (2017), 1701-1715.
doi: 10.1002/mana.201600180. |
[6] |
C. Jin,
Periodic pattern formation in the coupled chemotaxis-(Navier-)Stokes system with mixed nonhomogeneous boundary conditions, Proc. Roy. Soc. Edinb. Sect. A, 150 (2020), 3121-3152.
doi: 10.1017/prm.2019.62. |
[7] |
C. Liu and P. Li,
Global existence for a chemotaxis-haptotaxis model with p-Laplacian, Commun. Pure Appl. Anal., 19 (2020), 1399-1419.
doi: 10.3934/cpaa.2020070. |
[8] |
C. Liu and P. Li,
Time periodic solutions for a two-species chemotaxis-Navier-Stokes system, Discret. Contin. Dynam. Syst. Series B., 26 (2021), 4567-4585.
doi: 10.3934/dcdsb.2020303. |
[9] |
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. |
[10] |
N. Mizoguchi and P. Souplet,
Nondegeneracy of blow-up points for the parabolic Keller-Segel system, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 851-875.
doi: 10.1016/j.anihpc.2013.07.007. |
[11] |
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. |
[12] |
W. Tao and Y. Li,
Boundedness of weak solutions of a chemotaxis-Stokes system with slow p-Laplacian diffusion, J. Differ. Equ., 268 (2020), 6872-6919.
doi: 10.1016/j.jde.2019.11.078. |
[13] |
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. |
[14] |
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. |
[15] |
M. Winkler,
Global large-data solutions in a chemotaxis-Navier-Stokes system modeling cellular swimming in fluid drops, Commun. Partial Differ. Equ., 37 (2012), 319-351.
doi: 10.1080/03605302.2011.591865. |
[16] |
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. |
[17] |
M. Winkler,
Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differ. Equ., 248 (2010), 2889-2905.
doi: 10.1016/j.jde.2010.02.008. |
[18] |
J. Yin and C. Jin,
Periodic solutions of the evolutionary p-Laplacian with nonlinear sources, J. Math. Anal. Appl., 368 (2010), 604-622.
doi: 10.1016/j.jmaa.2010.03.006. |
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