Chemotaxis-fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior

By Marco Di Francesco, Alexander Lorz, Peter A. Markowich. 2010

265 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/723d34005f59e65e15d67491aa263b70ce837236

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Citations in the corpus

Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, background): “In [7], Francesco, Lorz and Markowich showed the global existence of a bounded solution to (7) on a bounded domain in R(2) with the boundary conditions ∂νn = ∂νc = u = 0 when m ∈ ( 3 2 , 2].”
Blow-up prevention by quadratic degradation in a two-dimensional Keller–Segel–Navier–Stokes system (2016, background): “nonlinear diffusion ([5], [33], [30], [31], [8]) and variants in the crossdiffusive term ([1], [34], [16]).”
A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, background): “In [15], global existence of solutions to the system (1.”
Global existence and boundedness in a 3D Keller–Segel–Stokes system with nonlinear diffusion and rotational flux (2017, background): “5) with κ = 1 for any m > 1 (see also [7,9,24,28,29,31,45] and references therein).”
The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system (2017, unknown): “1) ([7], [6], [21], [33], [34], [35], [29]).”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “For such models, numerous results have been achieved in the past few years, addressing topics ranging from the mere existence of global solutions ([13], [73], [3], [6]), also in the context of nonlinear cell diffusion ([14], [55], [60], [9], [77]), to global boundedness ([66], [5], [24], [4]) and ev”
How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system? (2015, background): “In the case m > 4 3 , global existence of – possibly unbounded – weak solutions has been established in [33] even for the associated full chemotaxis-Navier-Stokes system; results on global existence and boundedness in two-dimensional chemotaxis-fluid systems with nonlinear cell diffusion can be foun”
Global existence and boundedness in a Keller-Segel-Stokes model with arbitrary porous medium diffusion (2012, methodology): “From [3] we adopt the following solution concept.”
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, background): “also [7], [32], [11], [33] and [29] for results on related models with nonlinear diffusion).”