Global Solutions to the Coupled Chemotaxis-Fluid Equations

By Renjun Duan, Alexander Lorz, Peter A. Markowich. 2010

437 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f31bda2653a0c5c50f882a7bc572b9c9b4b25171

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cell Biology

In Modeling and Simulation

In Molecular Biology

Citations in the corpus

Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant (2012, background): “5), recent contributions assert global classical solutions near constant steady states when Ω = R3 ([5]), global weak solutions with arbitrarily large data in Ω = R2 ([13]), or global classical 3”
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”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, background): “Then still the understanding of the associated chemotaxis-only subsystem is far from complete especially in the case N = 3 ([29]), but the dampening effect of signal absorption at least under certain restrictions on the space dimension and the model parameter functions allows for the construction of”
Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, methodology): “Comparing with the result in [6], we show the local-in-time existence without smallness of the initial data.”
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.”
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, methodology): “Combined with appropriate regularization properties of the fluid flow, these may be used to derive a priori estimates which may form the starting point for global existence theories (see [10], [49], [39]) and also [29], for instance) as well as for the description of the large time asymptotics of so”
A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, background): “Moreover, in [16] the authors proved global existence for a simplified version of (1.”
Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system (2015, neutral): “[4], [28], [30] and [31], for instance).”
Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations (2013, background): “More precisely, [8] showed that if initial data n0 − n c0 u0 H3 is sufficiently small, then there exists a unique global solution, provided that”
The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system (2017, neutral): “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 weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion (2015, methodology): “The inequality is frequently used in the literature (see [6,20,29,30], for example) and it also will play an important role in our proof.”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “where the signal is produced by the cells under consideration and not ’only’ consumed, (CC1) along with its variants received renewed interest, when in the wake of experimental observations concerned with bacteria in drops of water [32, 109], starting from [85, 33] models coupling chemotaxis effects”