Boundedness in a chemotaxis model with oxygen consumption by bacteria

By Youshan Tao. 2011

312 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/7b3ca59e2a147151013c960186462f1cedb6ba64

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Citations in the corpus

Eventual smoothness and asymptotics in a three-dimensional chemotaxis system with logistic source (2014, background): “But not only the restriction to dimension 2, also the inclusion of some kind of saturation effect in the chemotactic sensitivity [2], sublinear dependence of the chemotactic sensitivity on u [3] or even changing the second equation into one that models the consumption of the chemoattractant (as done”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “4 ([104], [9]) Let n ≥ 2 and Ω ⊂ R be a bounded domain with smooth boundary, and suppose that u0 and v0 satisfy (2.”
Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D (2017, background): “. Obtaining results concerning the global existence of solutions is far from trivial, even when u≡ 0 the global existence of solutions is only known under a smallness condition on the initial data 2 ([26]), or when N= 2 (e.g. [35]). These outcomesare similarin the caseof u≡ 0. In the two-dimensional”
Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant (2012, methodology): “Independently, in [17] it has been proved that if in addition ‖v0‖L∞(Ω) is sufficiently small, then (1.”
Analysis of a chemotaxis model with indirect signal absorption (2019, background): “Tao [19] proved that whenever the corresponding initial data are sufficiently smooth and satisfy ‖v0‖L∞(Ω) ≤ 1 6(n+1) , then there exists a global classical solution of (1.”
Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis ✩ (2016, methodology): “We will use a weight function φ(v) similar to the one in [43,53] in the energy estimate.”
Very weak global solutions to a parabolic–parabolic chemotaxis-system with logistic source (2016, unknown): “We refer, for instance, to [4] and [29] for the parabolic-elliptic case and to [2], [3], [8], [13], [21] and [28] for the parabolic-parabolic one.”
Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations (2013, methodology): “We use the similar weighted energy estimate in [22], which treated the case that k are constants and fluid equation is absent.”
Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption (2016, background): “3) on the initial data ([15]) or in a two-dimensional setting ([ 22], [25] and also [9]).”
Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, unknown): “When u ≡ 0, χ(c) ≡ χ and k(c) ≡ c in (1), it was shown in [19] that there exists a uniquely global bounded solution if 0 < χ ≤ 1 6(d+ 1)‖c0‖L∞ .”