1 |
Y. Wang and Z. Xiang, Global existence and boundedness in a Keller-Segel-Stokes system involving a tensor-valued sensitivity with saturation: the 3D case, J. Differential Equations 261 (2016), no. 9, 4944-4973. https://doi.org/10.1016/j.jde.2016.07.010
DOI
|
2 |
M. Winkler, Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model, J. Differential Equations 248 (2010), no. 12, 2889-2905. https://doi.org/10.1016/j.jde.2010.02.008
DOI
|
3 |
M. Winkler, Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops, Comm. Partial Differential Equations 37 (2012), no. 2, 319-351. https://doi.org/10.1080/03605302.2011.591865
DOI
|
4 |
M. Winkler, Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity, Calc. Var. Partial Differential Equations 54 (2015), no. 4, 3789-3828. https://doi.org/10.1007/s00526-015-0922-2
DOI
|
5 |
M. Winkler, How far do chemotaxis-driven forces in uence regularity in the Navier-Stokes system?, Trans. Amer. Math. Soc. 369 (2017), no. 5, 3067-3125. https://doi.org/10.1090/tran/6733
DOI
|
6 |
M. Winkler, Does fluid interaction aect regularity in the three-dimensional Keller-Segel system with saturated sensitivity?, J. Math. Flfluid Mech. 20 (2018), no. 4, 1889-1909. https://doi.org/10.1007/s00021-018-0395-0
DOI
|
7 |
M. Winkler, Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement, J. Differential Equations 264 (2018), no. 10, 6109-6151. https://doi.org/10.1016/j.jde.2018.01.027
DOI
|
8 |
Q. Zhang and Y. Li, Global boundedness of solutions to a two-species chemotaxis system, Z. Angew. Math. Phys. 66 (2015), no. 1, 83-93. https://doi.org/10.1007/s00033-013-0383-4
DOI
|
9 |
T. Black, Global very weak solutions to a chemotaxis-fluid system with nonlinear diffusion, SIAM J. Math. Anal. 50 (2018), no. 4, 4087-4116. https://doi.org/10.1137/17M1159488
DOI
|
10 |
X. Bai and M. Winkler, Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics, Indiana Univ. Math. J. 65 (2016), no. 2, 553-583. https://doi.org/10.1512/iumj.2016.65.5776
DOI
|
11 |
N. Bellomo, A. Bellouquid, Y. Tao, and M. Winkler, Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues, Math. Models Methods Appl. Sci. 25 (2015), no. 9, 1663-1763. https://doi.org/10.1142/S021820251550044X
DOI
|
12 |
D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, 840, Springer-Verlag, Berlin, 1981.
|
13 |
X. Cao, Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term, J. Differential Equations 261 (2016), no. 12, 6883-6914. https://doi.org/10.1016/j.jde.2016.09.007
DOI
|
14 |
X. Cao, S. Kurima, and M. Mizukami, Global existence an asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics, Math. Methods Appl. Sci. 41 (2018), no. 8, 3138-3154. https://doi.org/10.1002/mma.4807
DOI
|
15 |
X. Cao, S. Kurima, and M. Mizukami, Global existence and asymptotic behavior of classical solutions for a 3D two-species Keller-Segel-Stokes system with competitive kinetics, preprint.
|
16 |
M. A. Herrero and J. J. L. Velazquez, A blow-up mechanism for a chemotaxis model, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 24 (1997), no. 4, 633-683.
|
17 |
M. Hirata, S. Kurima, M. Mizukami, and T. Yokota, Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics, J. Differential Equations 263 (2017), no. 1, 470-490. https://doi.org/10.1016/j.jde.2017.02.045
DOI
|
18 |
S. Ishida, K. Seki, and T. Yokota, Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains, J. Differential Equations 256 (2014), no. 8, 2993-3010. https://doi.org/10.1016/j.jde.2014.01.028
DOI
|
19 |
M. Hirata, S. Kurima, M. Mizukami, and T. Yokota, Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics, Proceedings of EQUADIFF 2017 Conference, (2017) 11-20.
|
20 |
D. Horstmann and M. Winkler, Boundedness vs. blow-up in a chemotaxis system, J. Differential Equations 215 (2005), no. 1, 52-107. https://doi.org/10.1016/j.jde.2004.10.022
DOI
|
21 |
X. Li, Global classical solutions in a Keller-Segel(-Navier)-Stokes system modeling coral fertilization, J. Differential Equations, In press.
|
22 |
E. F. Keller and L. A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theoret. Biol. 26 (1970), no. 3, 399-415. https://doi.org/10.1016/0022-5193(70)90092-5
DOI
|
23 |
O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type (Russian), Translated from the Russian by S. Smith. Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, RI, 1968.
|
24 |
H. Li and Y. Tao, Boundedness in a chemotaxis system with indirect signal production and generalized logistic source, Appl. Math. Lett. 77 (2018), 108-113. https://doi.org/10.1016/j.aml.2017.10.006
DOI
|
25 |
J. Liu and Y. Wang, Global existence and boundedness in a Keller-Segel-(Navier-)Stokes system with signal-dependent sensitivity, J. Math. Anal. Appl. 447 (2017), no. 1, 499-528. https://doi.org/10.1016/j.jmaa.2016.10.028
DOI
|
26 |
K. Lin, C. Mu, and L. Wang, Boundedness in a two-species chemotaxis system, Math. Methods Appl. Sci. 38 (2015), no. 18, 5085-5096. https://doi.org/10.1002/mma.3429
DOI
|
27 |
K. Lin, C. Mu, and H. Zhong, A new approach toward stabilization in a two-species chemotaxis model with logistic source, Comput. Math. Appl. 75 (2018), no. 3, 837-849. https://doi.org/10.1016/j.camwa.2017.10.007
DOI
|
28 |
J. Liu and Y. Wang, Boundedness and decay property in a three-dimensional Keller- Segel-Stokes system involving tensor-valued sensitivity with saturation, J. Differential Equations 261 (2016), no. 2, 967-999. https://doi.org/10.1016/j.jde.2016.03.030
DOI
|
29 |
J. Liu and Y. Wang, Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes system involving a tensor-valued sensitivity with saturation, J. Differential Equations 262 (2017), no. 10, 5271-5305. https://doi.org/10.1016/j.jde.2017.01.024
DOI
|
30 |
M. Mizukami, Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), no. 6, 2301-2319. https://doi.org/10.3934/dcdsb.2017097
|
31 |
M. Mizukami, Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), no. 6, 2301-2319. https://doi.org/10.3934/dcdsb.2017097
|
32 |
M. Negreanu and J. I. Tello, Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant, J. Differential Equations 258 (2015), no. 5, 1592-1617. https://doi.org/10.1016/j.jde.2014.11.009
DOI
|
33 |
M. Mizukami and T. Yokota, Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion, J. Differential Equations 261 (2016), no. 5, 2650-2669. https://doi.org/10.1016/j.jde.2016.05.008
DOI
|
34 |
T. Nagai, T. Senba, and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcial. Ekvac. 40 (1997), no. 3, 411-433.
|
35 |
M. Negreanu and J. I. Tello, On a two species chemotaxis model with slow chemical diffusion, SIAM J. Math. Anal. 46 (2014), no. 6, 3761-3781. https://doi.org/10.1137/140971853
DOI
|
36 |
G. Ren and B. Liu, Global boundedness and asymptotic behavior in a two-species chemotaxis-competition system with two signals, Nonlinear Anal. Real World Appl. 48 (2019), 288-325. https://doi.org/10.1016/j.nonrwa.2019.01.017
DOI
|
37 |
G. Ren and B. Liu, Global existence of bounded solutions for a quasilinear chemotaxis system with logistic source, Nonlinear Anal. Real World Appl. 46 (2019), 545-582. https://doi.org/10.1016/j.nonrwa.2018.09.020
DOI
|
38 |
G. Ren and B. Liu, Boundedness of solutions for a quasilinear chemotaxis-haptotaxis model, Hakkaido Mathematical Journal, Accepted.
|
39 |
C. Stinner, J. I. Tello, and M. Winkler, Competitive exclusion in a two-species chemotaxis model, J. Math. Biol. 68 (2014), no. 7, 1607-1626. https://doi.org/10.1007/s00285-013-0681-7
DOI
|
40 |
H. Sohr, The Navier-Stokes equations, Birkhauser Advanced Texts: Basler Lehrbucher., Birkhauser Verlag, Basel, 2001.
|
41 |
Y. Tao and M. Winkler, Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion, Ann. Inst. H. Poincare Anal. Non Lineaire 30 (2013), no. 1, 157-178. https://doi.org/10.1016/j.anihpc.2012.07.002
DOI
|
42 |
Y. Tao and M. Winkler, Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis-fluid system, Z. Angew. Math. Phys. 66 (2015), no. 5, 2555-2573. https://doi.org/10.1007/s00033-015-0541-y
DOI
|
43 |
Y. Tao and M. Winkler, Blow-up prevention by quadratic degradation in a two-dimensional Keller-Segel-Navier-Stokes system, Z. Angew. Math. Phys. 67 (2016), no. 6, Art. 138, 23 pp. https://doi.org/10.1007/s00033-016-0732-1
DOI
|
44 |
I. Tuval, L. Cisneros, C. Dombrowski, C. W. Wolgemuth, J. O. Kessler, and R. E. Goldstein, Bacterial swimming and oxygen transport near contact lines, Proc. Natl. Acad. Sci. 102 (2005), 2277-2282.
DOI
|
45 |
Y. Wang, Global weak solutions in a three-dimensional Keller-Segel-Navier-Stokes sys- tem with subcritical sensitivity, Math. Models Methods Appl. Sci. 27 (2017), no. 14, 2745-2780. https://doi.org/10.1142/S0218202517500579
DOI
|
46 |
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), no. 2, 421-466.
|
47 |
Y. Wang and Z. Xiang, Global existence and boundedness in a Keller-Segel-Stokes system involving a tensor-valued sensitivity with saturation, J. Differential Equations 259 (2015), no. 12, 7578-7609. https://doi.org/10.1016/j.jde.2015.08.027
DOI
|