A coupled chemotaxis-fluid model: Global existence

By Jian‐Guo Liu, Alexander Lorz. 2011

319 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/40d34ab536274df47ca89ebbca58d1cc88a972f2

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Citations in the corpus

A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, background): “Furthermore, in [27] and [34], global existence results without smallness assumptions are given.”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “If κ = μ = 0 (and f ≡ 0), this model is an instance of the one for which the existence of global weak solutions in Ω = R(2) was shown in [24].”
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, background): “also [24] for a precedent); in the case when moreover m > 8 7 and Ω is a bounded convex domain in R 3, the first component n of such a solution is in fact locally bounded in Ω̄ × [0,∞) ([31]), and if even m > 7 6 , then in the latter situation n actually remains bounded in all of Ω × (0,∞) ([38]).”
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion (2013, methodology): “Whereas the proofs in the mentioned previous related works [4,5,14,27] are crucially based on a free-energy inequality, our method will be different in that it will rely on a similar energy estimate only at a first stage.”
Stabilization in a two-dimensional chemotaxis-Navier–Stokes system (2013, unknown): “…so as to allow for the construction of unique global bounded classical solutions under the mild assumptions (1.8) and (1.9) on χ, f and (cid:4) [39]; (see also [20]), and to furthermore enforce stabilization of these solutions toward spatially homogeneous equilibria in the large time limit [41 .”
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, background): “The knowledge in this respect has become quite comprehensive in the spatially two-dimensional setting in which even Navier-Stokes fluid evolution may lead to global existence of uniquely determined classical solutions ([23], [39]); in the case N = 3, after all, certain global weak and at least event”
The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system (2017, unknown): “1) ([7], [6], [21], [33], [34], [35], [29]).”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, unknown): “The particular requirement therein that ‖c0‖L∞(R2) be small was later removed in [20] at the cost of additional structural hypotheses on χ and f .”
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”