논문KCI 등재
Asymptotic behaviors of solutions for an aerotaxis model coupled to fluid equations
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.
Abstract
We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.
참고문헌 (28)
- E. A. Carlen, "Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 22-D Navier-Stokes equation", Duke Math. J, 81(1), pp.135~157 (1995)
- A. Carpio, "Asymptotic behavior for the vorticity equations in dimensions two and three", Comm. Partial Differential Equations, 19(5-6), pp.827~872 (1994)
- M. Chae, "Existence of smooth solutions to coupled chemotaxis-fluid equations", Discrete Cont. Dyn. Syst. A, 33(6), pp.2271~2297 (2013)
- M. Chae, "Global existence and temporal decay in Keller-Segel models coupled to fiuid equations", Comm. Partial Diff. Equations, 39(7), pp.1205~1235 (2014)
- A. Chertock, "Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach", J. Fluid Mech, 694, pp.155~190 (2012)
- 정윤성, "GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A KELLER-SEGEL-FLUID MODEL WITH NONLINEAR DIFFUSION", 대한수학회지, 51(3), pp.635~654 (2014), 대한수학회
- R. Duan, "Global solutions to the coupled chemotaxis-fluid equations", Comm. Partial Differential Equations, 35(9), pp.1635~1673 (2010)
- M. D. Francesco, "Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: global existence and asymptotic behavior", Discrete Cont. Dyn. Syst. A, 28(4), pp.1437~1453 (2010)
- T. Gallay, "Global stability of vortex solutions of the two dimensional Navier-Stokes equation", Comm. Math. Phys, 255(1), pp.97~129 (2005)
- M. Giga, "Nonlinear Partial Differential Equations, Asymptotic Behavior of Solutions and Self-Similar Solutions" (2010), Birkhauser Boston
- M. Giga, "Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation", Comm. Math. Phys, 117(4), pp.549~568 (1988)
- M. A. Herrero, "A blow-up mechanism for a chemotaxis model", Ann. Sc. Norm. Super. Pisa Cl. Ser, 24(4), pp.633~683 (1997)
- D. Horstman, "From 1970 until present: The Keller-Segel model in chemotaxis and its consequences I", Jahresber. Deutsch. Math.-Verein, 105(3), pp.103~165 (2003)
- D. Horstman, "From 1970 until present: The Keller-Segel model in chemotaxis and its consequences II", Jahresber. Deutsch. Math.-Verein, 106(2), pp.51~69 (2004)
- W. J˝ager, "On explosions of solutions to s system of partial differential equations modeling chemotaxis", Trans. Amer. Math. Soc, 329(2), pp.819~824 (1992)
- E. F. Keller, "Initiation of slide mold aggregation viewd as an instability", J. Theor. Biol, 26(3), pp.399~415 (1970)
- E. F. Keller, "Model for chemotaxis", J. Theor. Biol, 30(2), pp.225~234 (1971)
- A. Lorz, "Coupled chemotaxis fluid model", Math. Models Methods Appl. Sci, 20(6), pp.987~1004 (2010)
- T. Nagai, "Applications of the Trudinger-Moser inequality to a parabolic system of chemotaxis", Funkcial Ekvac, 40(3), pp.411~433 (1997)
- Y. Naito, "Asymptotically self-similar solutions for the parabolic system modelling chemotaxis", Banach center publications, 74, pp.149~160 (2006)
- K. Osaki, "Finite dimensional attractors for one-dimensional Keller-Segel equations", Funkcial. Ekvac, 44(3), pp.441~469 (2001)
- C. S. Patlak, "Random walk with persistence and external bias", Bull. Math. Biophys, 15, pp.311~338 (1953)
- R. Schweyer, "Stable blow-up dynamic for the parabolic-parabolic Patlak-Keller-Segel model", arXiv:1403.4975v1, ~
- Y. Tao, "Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion", Discrete Cont. Dyn. Syst. A, 32(5), pp.1901~1914 (2012)
- I. Tuval, "Bacterial swimming and oxygen transport near contact lines", PNAS, 102(7), pp.2277~2282 (2005)
- M. Winkler, "Aggregation vs. global diffusive behavior in the higher-dimensional KellerSegel model", J. Differential Equations, 248(12), pp.2889~2995 (2012)
- M. Winkler, "Global large data solutions in a chemotaxis-(Navier-)Stokes system modeling cellular swimming in fluid drops", Comm. Partial Differential Equations, 37(2), pp.319~351 (2012)
- M. Winkler, "Stabilization in a two-dimensional chemotaxis-Navier-Stokes system", Arch. Ration. Mech. Anal, 211(2), pp.455~487 (2014)
관련 논문AI추천
GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A KELLER-SEGEL-FLUID MODEL WITH NONLINEAR DIFFUSION강경근, 김재우, 정윤성대한수학회 · 대한수학회지2014 · 제51권 제3호Global existence and asymptotic behavior in a three-dimensional two-species chemotaxis-Stokes system with tensor-valued sensitivityBin Liu, Guoqiang Ren대한수학회 · 대한수학회지2020 · 제57권 제1호Large time convergence for a chemotaxis model with degenerate local sensing and consumptionPhilippe Laurencot대한수학회 · 대한수학회보2024 · 제61권 제2호Large time behavior for the degenerate compressible Navier-Stokes equations with damping권영삼대한수학회 · 대한수학회보2019 · 제56권 제3호Global existence and asymptotic behavior of a two-species competitive fractional chemotaxis system on $\mathbb{R}^N$Ming Xu, Weiyi Zhang대한수학회 · 대한수학회보2025 · 제62권 제2호Global well-posedness for the 2D chemotaxis-Euler equations modeling coral fertilization대한수학회 · 대한수학회보2026 · 제63권 제1호
이 간행물의 다른 논문 (14건)
$\mathcal{W}$-resolutions and Gorenstein categories with respect to a semidualizing bimodulesXiaoyan Yangpp. 1-17Second-order symmetric duality in multiobjective programming over conesTilak Raj Gulati, Geeta Mehndirattapp. 19-25Global existence and blow-up for a degenerate reaction-diffusion system with nonlinear localized sources and nonlocal boundary conditionsFei Liangpp. 27-43On the strong law of large numbers for weighted sums of negatively superadditive dependent random variablesAiting Shenpp. 45-55Maximal inequalities and an application under a weak dependence신동완, 황은주pp. 57-72
