A Note on Global Existence for the Chemotaxis–Stokes Model with Nonlinear Diffusion

By Renjun Duan, Zhaoyin Xiang. 2014

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View Paper: https://www.semanticscholar.org/paper/73ee7f146fb0dd721fba23a434f65a4720599f31

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Citations in the corpus

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).”
Depleting the signal: Analysis of chemotaxis‐consumption models—A survey (2023, unknown): “2 ([34], [29], [30], [52], [149, Corollary 1.”
Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities (2016, background): “Due to the difficulties associated with the Navier-Stokes equations in three-dimensional domains, many of these works focus on the two-dimensional case ([60, 59, 46, 68, 66]) or more favorable variants of the model, for example by resorting to the Stokes equation upon neglection of the nonlinear con”
Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion (2015, methodology): “Recently, Duan and Xiang [7] generalized the global existence result for all exponents m ∈ [1,∞) .”
Stabilization in a two-dimensional chemotaxis-Navier–Stokes system (2013, unknown): “Indeed, if in the first equation the term ∆n is replaced by ∆n for m > 1, then, firstly, for any such choice ofm it is again possible to construct global weak solutions under appropriate assumptions on χ and f ([9]), but beyond this one can secondly prove local-in-time and even global boundedness of”
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”
Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, background): “2) obtained on replacing ∆n by nonlinear diffusion operators generalizing the porous medium-type choice ∆n for several ranges of m > 1 ([10], [33], [12], [48], [26], [43], [44], [56]).”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, background): “Other variants of the model that are commonly treated include nonlinear (porous medium type) diffusion of bacteria, where ∆n is replaced by ∆n for some m > 1 (see [34, 35, 10, 7, 49]), thereby improving chances for finding bounded solutions, or, exchanging χ∇ · (n∇c) for ∇ · (nS(n, c, x)∇c), more co”
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]).”