Global existence and boundedness in a Keller–Segel–Stokes system involving a tensor-valued sensitivity with saturation: The 3D case

By Yulan Wang, Zhaoyin Xiang. 2015

188 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/03bc59ac8d08c7924ccdcbdcc6d9d67985b85f05

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

Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement (2017, background): “An interesting open problem, partially addressed in [39] and [40], consists in determining optimal conditions on the interplay between these two mechanisms which indeed prevent explosions.”
Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities (2016, background): “erms stemming from integration by parts when dealing with an energy functional. By arguments relying on estimates from [25] or [37], it has become possible to remove this assumption (cf. [26] or also [52, 51, 24]). Since our approach does not involve such functionals, these terms will not arise in t”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “replaced by ∆nm 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 complex sensitivity functions S([46, 40, 39, 16, 5]), which may be matrix-valued, thus introducing new mathematical challenges by de”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, unknown): “5 in [36]) Let p ∈ [1,+∞) and r ∈ [1,+∞] be such that { r < 3p 3−2p if p ≤ 32 r ≤ ∞ if p > 32 .”
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, background): “1) accounting for signal production rather than consumption through cells, to a considerable extent relies on the use of a corresponding energy functional ([25], [17], [40]), and accordingly in this latter context only few results, exclusively relying on quite strong assumptions on the system ingred”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “1) involving some inhibition of chemotactic cross-diffusion at large cell or signal densities, results on global existence and partially also on boundedness in two- and three-dimensional settings have recently been established in [61] and [62] as well as in [39], [40] and [41].”