Existence of Local Solution for an Attraction-Repulsion Chemotaxis System with Nonlinear Diffusion and Logistic Source
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Abstract
In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous compressible fluid equations through transport and external forcing. The local existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the an attraction-repulsion chemotaxis model system over three space dimensions, we obtain local existence and uniqueness of convergence on classical solutions near constant states. we prove local existence of unique solutions in three dimensions by using energy estimate
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References
E. Keller, L. Segel, Initiation of slime mold aggregation viewed as an
instability J. Theoret. Biol., pp. 399-415, 1970.
E. Keller, L. Segel, Model for chemotaxisJ. Theoret. Biol., pp. 225-234, 1971[3] D. Ambrosi, F. Bussolino and L. Preziosi, A review of vasculogenesis models. Theoretical Medicine. 6, 1-19, 2005.
M. Chae, K. Kang, and J. Lee, Existence of smooth solutions to chemotaxis-fluid equations, Discrete and continuous dynamical systems. 33, 2271-2297, 2013.
T. Yokota and N. Yoshino, Existence of solutions to chemotaxis dynamics with Lipschitz diffusion and superliear growth J. Math. Anal. Appl., 419, 756-774, 2014.
Corrias L, Perthame B, Zaag H. A chemotaxis model motivated by angiogenesis. CR Math. 336, p141-146, 2003.
Corrias L, Perthame B, Zaag H. Global solutions of some chemotaxis and angiogenesis systems in high space dimensions. Milan J Math.;72:1-28, 2004.
Y. Kagei and S. Kawashima, Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space, Comm. Math. Phys., 266 (2006), 401–430, 2006.
S. Kawashima, Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Doctoral Thesis, Kyoto University, 1983.
Wenjie L. Jinde C. Guodong L. Fei X. Dynamics analysis of a diffusive SIRI epidemic system under logistic source and general incidence rate, Communications in Nonlinear Science and Numerical Simulation Volume 129, February, 107675, 2024.
Y. Kagei and T. Kobayashi, Asymptotic behavior of solutions to the compressible Navier-Stokes equations on the half space, Arch. Rational Mech. Anal., 177. 231–330, 2005.
Kozono H, Sugiyama Y. Global strong solution to the semi-linear Keller–Segel system of parabolic-parabolic type with small data in scale invariant spaces. J Differential Equations. 247:1-32, 2009.
L. lin, C Qian. Global well posedness of chemotaxis Navier Stokes system with refined rough initial data in R^d, Nonlinear Analysis. Real world Applications, 2024
Z.A. Wang et al, Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis J. Differ. Equ.2225-2358, 260, 2016.
M. Winkler and K. C. Djie, Boundedness and nite-time collapse in a chemotaxis system with volume lling Nonlinear Anal., 72,1044-1064, 2010.
Z. Tan and J. Zhou, Global existence and time decay estimate of solutions to the Keller- Segel system, Math Meth Appl. Sci., 42, 375-402, 2019.
R. Duan, A. Lorz, and P. Markowich, Global solutions to the coupled chemotaxis-fluid equations, Comm. Partial Diff. Equations, 35, 1635-1673, 2010.
A. D. Rodriguez, L.C.F. Ferreira and E.J. Villamizar-Roa, Global existence for an attraction-repulsion chemotaxis fluid model with logistic source. Discrete Contin. Dyn. Syst. Ser. B, 23, 557-571, 2018.
A. Matsumura, An energy method for the equations of motion of compressible viscous and heat-conductive fluids, University of Wisconsin-Madison, MRC Technical Summary Report. N2194 1–16, 1981.
H. Hattori and A. Lagha, Existence of global solutions to chemotaxis fluid system with logistic source.vol.2022.No.01-87, 2021.
H. Hattori and A. Lagha, Global Existence and Decay Rates of the Solutions for a Chemotaxis System Lotka-Volterra Type Model for Chemo Agents. Discrete and Continuous Dynamical Systems 2021, Volume 41, 2021.
L. Xiao and M. Li, “Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations.” Boundary Value Problems, vol. 2021, no. 1, pp. 1–24, 2020.
A. Matsumura and T. Nishida. The Initial Value Problem for
the Equations of Motion of Viscous and Heat Conductive Gases.
Journal of Mathematics of Kyoto University, 20(1):67–104, 1980.