Electronic Research Archive

2021, Issue 5: 3509-3533. doi: 10.3934/era.2021050

Global existence for a two-species chemotaxis-Navier-Stokes system with $p$-Laplacian

• Received: 01 February 2021 Revised: 01 May 2021 Published: 22 July 2021
• Primary: 92C17, 35K51; Secondary: 35K65, 35K92

• We consider a two-species chemotaxis-Navier-Stokes system with $p$-Laplacian in three-dimensional smooth bounded domains. It is proved that for any $p\geq2$, the problem admits a global weak solution.

Citation: Jiayi Han, Changchun Liu. Global existence for a two-species chemotaxis-Navier-Stokes system with $p$-Laplacian[J]. Electronic Research Archive, 2021, 29(5): 3509-3533. doi: 10.3934/era.2021050

Related Papers:

• We consider a two-species chemotaxis-Navier-Stokes system with $p$-Laplacian in three-dimensional smooth bounded domains. It is proved that for any $p\geq2$, the problem admits a global weak solution.

 [1] Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics. Indiana Univ. Math. J. (2016) 65: 553-583. [2] Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues. Math. Models Methods Appl. Sci. (2015) 25: 1663-1763. [3] Global existence and asymptotic behavior of classical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics. Math. Meth. Appl. Sci. (2018) 41: 3138-3154. [4] On a fourth-order degenerate parabolic equation: global entropy estimates, existence, and qualitative behavior of solutions. SIAM J. Math. Anal. (1998) 29: 321-342. [5] Existence and uniqueness of local classical solutions to modified tumor invasion models of Chaplain-Anderson type. Adv. Math. Sci. Appl. (2014) 24: 67-84. [6] Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier-Stokes system with competitive kinetics. J. Differential Equations (2017) 263: 470-490. [7] Boundedness and global solvability to a chemotaxis-haptotaxis model with slow and fast diffusion. Discrete Contin. Dyn. Syst. Ser. B (2018) 23: 1675-1688. [8] Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics. Discrete Contin. Dyn. Syst. Ser. B (2019) 24: 1919-1942. [9] J.-L. Lions, Quelques méthodes de résolution des problémes aux limites non linéaires, Dunod, Gauthier-Villars, Paris, 1969. [10] J. Liu, Boundedness in a chemotaxis-Navier-Stokes System modeling coral fertilization with slow $p$-Laplacian diffusion, J. Math. Fluid Mech., 22 (2020), No. 10, 31 pp. doi: 10.1007/s00021-019-0469-7 [11] Global existence for a chemotaxis-haptotaxis model with $p$-Laplacian. Commun. Pure Appl. Anal. (2020) 19: 1399-1419. [12] C. Liu and P. Li, Boundedness and global solvability for a chemotaxis-haptotaxis model with $p$-Laplacian diffusion, Electron. J. Differential Equations, (2020), Paper No. 16, 16 pp. [13] Time periodic solutions for a two-species chemotaxis-Navier-Stokes system. Discrete and Continuous Dynamical Systems Series B (2021) 26: 4567-4585. [14] On energy inequality, smoothness and large time behaviour in $L^2$ for weak solutions of the Navier-Stokes equations in exterior domains. Math. Z. (1988) 199: 455-478. [15] Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity. Discrete Contin. Dyn. Syst. Ser. B (2017) 22: 2301-2319. [16] On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (1959) 13: 115-162. [17] H. Sohr, The Navier-Stokes Equations. An Elementary Functional Analytic Approach, Birkhäuser, Basel, 2001. [18] Global weak solutions in a PDE-ODE system modeling multiscale cancer cell invasion. SIAM J. Math. Anal. (2014) 46: 1969-2007. [19] Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion. Nonlinear Anal. Real World Appl. (2019) 45: 26-52. [20] Boundedness of weak solutions of a chemotaxis-Stokes system with slow $p$-Laplacian diffusion. J. Differential Equations (2020) 268: 6872-6919. [21] Bacterial swimming and oxygen transport near contact lines. Proc. Natl. Acad. Sci. USA (2005) 102: 2277-2282. [22] Global weak solutions in a three-dimensional chemotaxis-Navier-Stokes system. Ann. Inst. H. Poincaré Anal. Non Linéaire (2016) 33: 1329-1352. [23] Global large-data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops. Comm. Partial Differential Equations (2012) 37: 319-351. [24] Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model. J. Differential Equations (2010) 248: 2889-2905. [25] How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?. Trans. Amer. Math. Soc. (2017) 369: 3067-3125.
通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

1.604 0.8