Existence and uniqueness theorem on mild solutions to the Keller–Segel system coupled with the Navier–Stokes fluid

By H. Kozono, M. Miura, Yoshie Sugiyama. 2016

145 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/53b1fcf6e3af6c67aa27a748836e9b0206f96e0e

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Citations in the corpus

Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities (2016, methodology): “Unlike the study of mild solutions to a Keller-Segel-Navier-Stokes system in [28], we are concerned with bounded domains and admit non-scalar sensitivities.”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “Beyond a result on global existence of certain small-data solutions ([31]), the apparently first analytical result in this context which addresses large initial data asserts global existence of certain weak solutions in a two-dimensional simplification of (1.”
The small-convection limit in a two-dimensional chemotaxis-Navier–Stokes system (2017, unknown): “In full chemotaxis-Navier–Stokes systems, further boundedness properties could only be established upon imposing appropriate smallness conditions on the initial data [2,4,5,7,18,26,42].”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, background): “Although with few exceptions ([30], [49]) in threedimensional versions and further variants of (1.”
Local energy estimates and global solvability in a three-dimensional chemotaxis-fluid system with prescribed signal on the boundary (2021, background): “Extensions in various directions are concerned with global classical solvability for small data [13, 14], or address modified systems involving nonlinear cell diffusion of porous medium type [15–19], or also accounting for saturation effects in chemotactic migration [20–22].”
Global mass-preserving solutions in a two-dimensional chemotaxis-Stokes system with rotational flux components (2018, background): “1) in various functional frameworks, either in bounded two- or three-dimensional domains, or in the respective entire spaces, and under diverse, more or less restrictive assumptions on the parameter functions S, f and φ ([10], [5], [20], [39]; cf.”
Global existence and stabilization in a degenerate chemotaxis-Stokes system with mildly strong diffusion enhancement (2017, background): “2) with D ≡ 1, global smooth and bounded solutions could be shown to exist only under appropriate smallness assumptions on the initial data ([11], [23], [7], [6]), while for arbitrarily large data so far only certain global weak solutions have been constructed, which do become smooth eventually but ”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “In Ω = R(3), mild solutions to a system encompassing both mechanisms at the same time were proven to exist under a smallness condition on initial data ([20]).”