Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion

By Youshan Tao, Michael Winkler. 2013

248 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/808b7ff9dd58e38d5a0f19c15027d0dbdbef14f1

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Citations in the corpus

Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, methodology): “also [7], [32], [11], [33] and [29] for results on related models with nonlinear diffusion).”
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]).”
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”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “Other variants of the model that are commonly treated include nonlinear (porous medium type) diffusion of bacteria, where ∆n is replaced by ∆n for some m > 1 (see [34, 35, 10, 7, 49]), thereby improving chances for finding bounded solutions, or, exchanging χ∇ · (n∇c) for ∇ · (nS(n, c, x)∇c), more co”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, background): “nonlinear diffusion ([5], [33], [30], [31], [8]) and variants in the crossdiffusive term ([1], [34], [16]).”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, unknown): “1 goes considerably beyond the outcome in [29] in that, inter alia, global boundedness, rather than merely local boundedness, of solutions is obtained here.”
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement (2017, background): “This partially extended a precedent result which asserted global solvability within the larger range m > 8 7 , but only in a class of weak solutions locally bounded in Ω× [0,∞) ([34]).”
Stabilization in a two-dimensional chemotaxis-Navier–Stokes system (2013, unknown): “…appropriate assumptions on χ and f [10], but beyond this one can secondly prove local-in-time and even global boundedness of these solutions in the cases m > 87 and m 76 , respectively, and thereby rule out the occurrence of blow-up in ﬁnite time, and also in inﬁnite time (cf. [ 33] and [42] .”