COUPLED CHEMOTAXIS FLUID MODEL

By Alexander Lorz. 2010

246 citations recorded by the source corpus.

Subfields: Computational Mechanics, Condensed Matter Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/9aaa82d87ca2905e23eb0bc836c4eb3bfb7d0e4d

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Citations in the corpus

Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior (2010, background): “6) there is a local existence result [20].”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, unknown): “We refer to [8,10,24,29,30,46] and references therein for the nonlinear diffusion models of a porous medium type Δn, instead of Δn.”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, background): “where the signal is produced by the cells under consideration and not ’only’ consumed, (CC1) along with its variants received renewed interest, when in the wake of experimental observations concerned with bacteria in drops of water [32, 109], starting from [85, 33] models coupling chemotaxis effects”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, unknown): “1) its evolution is described by the Stokes equations rather than the full Navier–Stokes system [21].”
Analysis of a chemotaxis model with indirect signal absorption (2019, background): “For instance, coupled chemotaxis-fluid systems [14, 26, 29, 28], systems with nonlinear diffusion and/or nonlinear chemotactic sensitivity [3, 9, 13, 31] or systems with zeroth order terms accounting for logistic growth [10] or competition between species [23] have been analyzed.”
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion (2012, background): “In [13] the author proved local existence of solutions to (1.”
Suppression of Chemotactic Explosion by Mixing (2015, background): “Moreover, in a series of papers [27], [10], [9], [26], [28] a very interesting problem coupling chemotactic density with fluid mechanics equations actively forced by this density has been considered in a variety of different settings.”
Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops (2012, background): “1) is nonzero, the fluid motion is governed by the full Navier–Stokes equations involving nonlinear convection, whereas if = 0 we consider the simplified Stokes evolution for u which appears to be justified if the fluid flow remains small [15].”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “This assumption is less natural, at least for the part of the boundary that separates water and air, but so far has been employed in almost all papers dealing with chemotaxis fluid interaction from a mathematical viewpoint (exceptions being early existence results for weak solutions in 2-dimensional”
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, unknown): “1) in the physical domain Ω ⊂ R ([31], [24]).”
Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, methodology): “In [13], Liu and Lorz proved the global existence of a weak solution to (7) in R3 when m = 43 .”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, unknown): “also [42] for an early approach), where if Tmax,ε <∞, then for all q > 3 and α ∈ (34 , 1), ‖nε(·, t)‖L∞(Ω) + ‖cε(·, t)‖W 1,q(Ω) + ‖Auε(·, t)‖L2(Ω) → ∞ as tր Tmax,ε; (3.”