Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations

By Myeongju Chae, Kyungkeun Kang, Jihoon Lee. 2013

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We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that equations of oxygen concentration is of parabolic or hyperbolic type. We also prove that solutions exist globally in time and upper bounds of temporal decays are obtained under the some smallness conditions of initial data.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/989543f148a9e557da0ff39b158cfb8a77c70532

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Citations in the corpus

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A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “For such models, numerous results have been achieved in the past few years, addressing topics ranging from the mere existence of global solutions ([13], [73], [3], [6]), also in the context of nonlinear cell diffusion ([14], [55], [60], [9], [77]), to global boundedness ([66], [5], [24], [4]) and ev”
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, background): “Concerning the large time behavior of solutions, only very few seems known even in simplified situations: Except for some results on convergence of solutions satisfying certain smallness conditions ([9], [4]), the only statememts we are aware of which cover arbitrarily large initial data in (1.”
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The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system (2017, unknown): “In full chemotaxis-Navier–Stokes systems, further boundedness properties could only be established upon imposing appropriate smallness conditions on the initial data [2,4,5,7,18,26,42].”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, background): “Despite the known challenges arising from the theory of fluid equations and the study of chemotaxis systems, in the past several years there have been numerous analytical approaches that addressed issues of well-posedness for corresponding initial (boundary) value problems in either bounded or unbou”