This paper proposes a survey and critical analysis focused on a variety of chemotaxis
models in biology, namely the classical Keller–Segel model and its subsequent …

In the modeling of collective effects arising in bacterial suspensions in fluid drops, coupled
chemotaxis-(Navier–) Stokes systems generalizing the prototype have been proposed to …

Abstract The chemotaxis–Navier–Stokes system (0.1){n t+ u⋅∇ n= Δ n−∇⋅(n χ (c)∇ c), c t+
u⋅∇ c= Δ c− nf (c), u t+(u⋅∇) u= Δ u+∇ P+ n∇ Φ,∇⋅ u= 0,(⋆) is considered under …

This paper deals with an initial-boundary value problem for the system\left {n_t+ u ⋅ ∇ n &=
& Δ n-∇ ⋅ (n χ (c) ∇ c),\quad\quad & x ∈ Ω,\, t> 0,\c_t+ u ⋅ ∇ c &= & Δ c-nf (c),\quad\quad & …

Abstract The Keller–Segel–Navier–Stokes system (⋆){n t+ u⋅∇ n= Δ n− χ∇⋅(n∇ c)+ ρ n− μ
n 2, c t+ u⋅∇ c= Δ c− c+ n, u t+(u⋅∇) u= Δ u+∇ P+ n∇ ϕ+ f (x, t),∇⋅ u= 0, is considered in …

The chemotaxis-Navier-Stokes system\begin {equation*}(\star)\qquad\qquad\qquad\quad\
begin {cases} n_t+ u\cdot\nabla n &=\\\Delta n-\nabla\cdot (n\chi (c)\nabla c),\\[1mm] c_t+ …

We consider the chemotaxis-fluid system 0.1 in a bounded convex domain Ω⊂ R 3 with
smooth boundary, where ϕ∈ W 1,∞(Ω) and D, f and S are given functions with values in …

This paper deals with positive solutions of under homogeneous Neumann boundary
conditions in bounded convex domains Ω⊂ R3 with smooth boundary. It is shown that for …

The coupled chemotaxis fluid system {n_t= Δ n-∇ ⋅ (n S (x, n, c) ⋅ ∇ c)-u ⋅ ∇ n, &\quad (x,
t) ∈ Ω * (0, T),\c_t= Δ c-nc-u ⋅ ∇ c, &\quad (x, t) ∈ Ω * (0, T),\u_t= Δ u-(u ⋅ ∇) u+ ∇ P+ n ∇ …

We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations
in spatial dimensions two and three. We establish the local existence of regular solutions …