Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant

By Youshan Tao, Michael Winkler. 2012

390 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/35f26015f0026cae769981c7cc8ba45230750db3

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Citations in the corpus

Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “In the case when Ω additionally is two-dimensional, this information on regularity of the taxis gradient in (CC1) can be used as a starting point for a boothstrap procedure finally leading not only to L∞ bounds for u, but furthermore also to a statement on large time stabilization ([105]).”
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”
Competing effects of attraction vs. repulsion in chemotaxis (2013, background): “This type of entropy inequality also plays an important role in a recent study of a chemotaxis system with consumption of chemoattractant.(49) Lemma 6.”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, neutral): “If this two-component system is further simplified by moreover choosing the sensitivity to be a constant scalar, again some energy arguments become available so as to yield much more comprehensive results on global existence of solutions and even on their large time behavior [27].”
The two-dimensional Keller–Segel system with singular sensitivity and signal absorption: Global large-data solutions and their relaxation properties (2016, background): “3) when posed in bounded domains in R with arbitrarily large initial data (u0, v0), possesses global bounded classical solutions in the case n = 2 and global weak solutions if n = 3 ([40]), whereas if n ≥ 3 then global bounded classical solutions can be found whenever ‖v0‖L∞(Ω) is suitably small ([3”
Analysis of a chemotaxis model with indirect signal absorption (2019, background): “In many cases, for instance in [10, 20, 21], the authors utilize the functional”
Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D (2017, background): “In particular, for the fluid free case eventual smoothness of solutions was shown in [27] for N = 3 and a result including fluid is contained in [40], where certain weak eventual energy solutions are considered.”