Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops

By Michael Winkler. 2012

716 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Condensed Matter Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/7d3d32bd9e6abc1fb7bac113e09dd58f6b283b8a

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In Biomedical Engineering

In Condensed Matter Physics

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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): “Combined with appropriate regularization properties of the fluid flow, these may be used to derive a priori estimates which may form the starting point for global existence theories (see [10], [49], [39]) and also [29], for instance) as well as for the description of the large time asymptotics of so”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, background): “Despite the known challenges arising from the theory of fluid equations and the study of chemotaxis systems, in the past several years there have been numerous analytical approaches that addressed issues of well-posedness for corresponding initial (boundary) value problems in either bounded or unbou”
Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, background): “That also the latter restriction can actually be relaxed was one of the results in [32], where a corresponding boundary value problem was considered in bounded convex domains (cf.”
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement (2017, methodology): “2) already in presence of linear cell diffusion, and even when the fluid flow is governed by the corresponding full nonlinear Navier-Stokes system ([11], [43], [45], [8], [49], see also [22]).”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, neutral): “valid actually for arbitrary bounded domains Ω ⊂ R with smooth boundary, and for any positive φ ∈ C2(Ω) such that ∂φ ∂ν |∂Ω = 0 ([141]), in the convex case an integration of (2.”
A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, background): “Furthermore, in [27] and [34], global existence results without smallness assumptions are given.”
Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, background): “(5) Very recently, Winkler[23] considered the equations (1) on a bounded domain Ω in R(2) with the boundary condition ∂νn = ∂νc = u = 0 on ∂Ω, and proved the global-in-time existence of a classical solution under the assumption such that χ(c) > 0, k(c) ≥ 0, ( k(c) χ(c) )′ > 0, (χ(c)k(c))′ ≥ 0, and d”
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”
Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary (2021, background): “[10] or [11], for instance); a slight difference to most precedents consists in the artificial e-dependent dampening expressed in the source term FeðneÞr/ entering the Stokes subsystem of (2.”
A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity (2015, methodology): “Functionals containing this term have successfully been used in the context of coupled chemotaxis-fluid systems (see [16]) or of chemotaxis models with consumption of the chemoattractant [17] (e.”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, background): “on c ([11]), and also for a corresponding boundary-value problem in bounded convex three-dimensional domains without imposing any such additional requirements ([53]).”