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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.
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참고문헌 (28)
참고문헌 신청
E. A. Carlen / 1995 / Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 22-D Navier-Stokes equation / Duke Math. J 81(1):135~157
A. Carpio / 1994 / Asymptotic behavior for the vorticity equations in dimensions two and three / Comm. Partial Differential Equations 19(5-6):827~872
M. Chae / 2013 / Existence of smooth solutions to coupled chemotaxis-fluid equations / Discrete Cont. Dyn. Syst. A 33(6):2271~2297
M. Chae / 2014 / Global existence and temporal decay in Keller-Segel models coupled to fiuid equations / Comm. Partial Diff. Equations 39(7):1205~1235
A. Chertock / 2012 / Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach / J. Fluid Mech 694:155~190
A. Carpio / 1994 / Asymptotic behavior for the vorticity equations in dimensions two and three / Comm. Partial Differential Equations 19(5-6):827~872
M. Chae / 2013 / Existence of smooth solutions to coupled chemotaxis-fluid equations / Discrete Cont. Dyn. Syst. A 33(6):2271~2297
M. Chae / 2014 / Global existence and temporal decay in Keller-Segel models coupled to fiuid equations / Comm. Partial Diff. Equations 39(7):1205~1235
A. Chertock / 2012 / Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach / J. Fluid Mech 694:155~190
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