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In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neumann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some $L^p$-estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addition to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.
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참고문헌 (46)
참고문헌 신청
X. Bai / 2016 / Equilibration in a fully parabolic two-species chemotaxis system with competitive kinetics / Indiana Univ. Math. J 65(2):553~583
T. Black / 2018 / Global very weak solutions to a chemotaxis-uid system with nonlinear dif-fusion / SIAM J. Math. Anal 50(4):4087~4116
N. Bellomo / 2015 / Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues / Math. Models Methods Appl. Sci 25(9):1663~1763
X. Cao / 2016 / Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational ux term / J. Dierential Equations 261(12):6883~6914
X. Cao / 2018 / Global existence an asymptotic behavior of clas-sical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics / Math. Methods Appl. Sci. 41(8):3138~3154
T. Black / 2018 / Global very weak solutions to a chemotaxis-uid system with nonlinear dif-fusion / SIAM J. Math. Anal 50(4):4087~4116
N. Bellomo / 2015 / Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues / Math. Models Methods Appl. Sci 25(9):1663~1763
X. Cao / 2016 / Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational ux term / J. Dierential Equations 261(12):6883~6914
X. Cao / 2018 / Global existence an asymptotic behavior of clas-sical solutions for a 3D two-species chemotaxis-Stokes system with competitive kinetics / Math. Methods Appl. Sci. 41(8):3138~3154
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