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Convergence rates of solutions for a two-dimensional chemotaxis-Navier-Stokes system
1. | Department of Mathematics, Southeast University, Nanjing 211189, China, China |
References:
[1] |
M. Chae, K. Kang and J. Lee, Existence of smooth solutions to coupled chemotaxis-fluid equations,, Discrete Contin. Dyn. Syst., 33 (2013), 2271.
doi: 10.3934/dcds.2013.33.2271. |
[2] |
M. Chae, K. Kang and J. Lee, Global existence and temporal decay in Keller-Segel models coupled to fluid equations,, Comm. Partial Differential Equations, 39 (2014), 1205.
doi: 10.1080/03605302.2013.852224. |
[3] |
M. Di Francesco, A. Lorz and P. Markowich, Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior,, Discrete Contin. Dyn. Syst., 28 (2010), 1437.
doi: 10.3934/dcds.2010.28.1437. |
[4] |
R. Duan, A. Lorz and P. Markowich, Global solutions to the coupled chemotaxis-fluid equations,, Comm. Partial Differential Equations, 35 (2010), 1635.
doi: 10.1080/03605302.2010.497199. |
[5] |
R. Duan and Z. Xiang, A note on global existence for the chemotaxis-Stokes model with nonlinear diffusion,, Int. Math. Res. Not. IMRN, (2014), 1833.
|
[6] |
J. Jiang, H. Wu and S. Zheng, Global existence and asymptotic behavior of solutions to a chemotaxis-fluid system on general bounded domain,, preprint, (). Google Scholar |
[7] |
J.-G. Liu and A. Lorz, A coupled chemotaxis-fluid model: Global existence,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28 (2011), 643.
doi: 10.1016/j.anihpc.2011.04.005. |
[8] |
A. Lorz, Coupled chemotaxis fluid model,, Math. Models Methods Appl. Sci., 20 (2010), 987.
doi: 10.1142/S0218202510004507. |
[9] |
A. Lorz, A coupled Keller-Segel-Stokes model: Global existence for small initial data and blow-up delay,, Commun. Math. Sci., 10 (2012), 555.
doi: 10.4310/CMS.2012.v10.n2.a7. |
[10] |
Y. Tao and M. Winkler, Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion,, Discrete Contin. Dyn. Syst., 32 (2012), 1901.
doi: 10.3934/dcds.2012.32.1901. |
[11] |
Y. Tao and M. Winkler, Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 157.
doi: 10.1016/j.anihpc.2012.07.002. |
[12] |
I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J. O. Kessler and R. E. Goldstein, Bacterial swimming and oxygen transport near contact lines,, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), 2277.
doi: 10.1073/pnas.0406724102. |
[13] |
M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model,, J. Differential Equations, 248 (2010), 2889.
doi: 10.1016/j.jde.2010.02.008. |
[14] |
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.
doi: 10.1080/03605302.2011.591865. |
[15] |
M. Winkler, Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening,, J. Differential Equations, 257 (2014), 1056.
doi: 10.1016/j.jde.2014.04.023. |
[16] |
M. Winkler, Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system,, preprint, (). Google Scholar |
[17] |
M. Winkler, Stabilization in a two-dimensional chemotaxis-Navier-Stokes system,, Arch. Ration. Mech. Anal., 211 (2014), 455.
doi: 10.1007/s00205-013-0678-9. |
[18] |
Q. Zhang, Local well-posedness for the chemotaxis-Navier-Stokes equations in Besov spaces,, Nonlinear Anal. Real World Appl., 17 (2014), 89.
doi: 10.1016/j.nonrwa.2013.10.008. |
[19] |
Q. Zhang and X. Zheng, Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations,, SIAM J. Math. Anal., 46 (2014), 3078.
doi: 10.1137/130936920. |
show all references
References:
[1] |
M. Chae, K. Kang and J. Lee, Existence of smooth solutions to coupled chemotaxis-fluid equations,, Discrete Contin. Dyn. Syst., 33 (2013), 2271.
doi: 10.3934/dcds.2013.33.2271. |
[2] |
M. Chae, K. Kang and J. Lee, Global existence and temporal decay in Keller-Segel models coupled to fluid equations,, Comm. Partial Differential Equations, 39 (2014), 1205.
doi: 10.1080/03605302.2013.852224. |
[3] |
M. Di Francesco, A. Lorz and P. Markowich, Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior,, Discrete Contin. Dyn. Syst., 28 (2010), 1437.
doi: 10.3934/dcds.2010.28.1437. |
[4] |
R. Duan, A. Lorz and P. Markowich, Global solutions to the coupled chemotaxis-fluid equations,, Comm. Partial Differential Equations, 35 (2010), 1635.
doi: 10.1080/03605302.2010.497199. |
[5] |
R. Duan and Z. Xiang, A note on global existence for the chemotaxis-Stokes model with nonlinear diffusion,, Int. Math. Res. Not. IMRN, (2014), 1833.
|
[6] |
J. Jiang, H. Wu and S. Zheng, Global existence and asymptotic behavior of solutions to a chemotaxis-fluid system on general bounded domain,, preprint, (). Google Scholar |
[7] |
J.-G. Liu and A. Lorz, A coupled chemotaxis-fluid model: Global existence,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 28 (2011), 643.
doi: 10.1016/j.anihpc.2011.04.005. |
[8] |
A. Lorz, Coupled chemotaxis fluid model,, Math. Models Methods Appl. Sci., 20 (2010), 987.
doi: 10.1142/S0218202510004507. |
[9] |
A. Lorz, A coupled Keller-Segel-Stokes model: Global existence for small initial data and blow-up delay,, Commun. Math. Sci., 10 (2012), 555.
doi: 10.4310/CMS.2012.v10.n2.a7. |
[10] |
Y. Tao and M. Winkler, Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion,, Discrete Contin. Dyn. Syst., 32 (2012), 1901.
doi: 10.3934/dcds.2012.32.1901. |
[11] |
Y. Tao and M. Winkler, Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 30 (2013), 157.
doi: 10.1016/j.anihpc.2012.07.002. |
[12] |
I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J. O. Kessler and R. E. Goldstein, Bacterial swimming and oxygen transport near contact lines,, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005), 2277.
doi: 10.1073/pnas.0406724102. |
[13] |
M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model,, J. Differential Equations, 248 (2010), 2889.
doi: 10.1016/j.jde.2010.02.008. |
[14] |
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.
doi: 10.1080/03605302.2011.591865. |
[15] |
M. Winkler, Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening,, J. Differential Equations, 257 (2014), 1056.
doi: 10.1016/j.jde.2014.04.023. |
[16] |
M. Winkler, Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system,, preprint, (). Google Scholar |
[17] |
M. Winkler, Stabilization in a two-dimensional chemotaxis-Navier-Stokes system,, Arch. Ration. Mech. Anal., 211 (2014), 455.
doi: 10.1007/s00205-013-0678-9. |
[18] |
Q. Zhang, Local well-posedness for the chemotaxis-Navier-Stokes equations in Besov spaces,, Nonlinear Anal. Real World Appl., 17 (2014), 89.
doi: 10.1016/j.nonrwa.2013.10.008. |
[19] |
Q. Zhang and X. Zheng, Global well-posedness for the two-dimensional incompressible chemotaxis-Navier-Stokes equations,, SIAM J. Math. Anal., 46 (2014), 3078.
doi: 10.1137/130936920. |
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