This paper proposes a review focused on exotic chemotaxis and cross-diffusion models in
complex environments. The term exotic is used to denote the dynamics of models interacting …

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 …

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 & …

We consider radially symmetric solutions of the Keller–Segel system with generalized
logistic source given by {u_t= Δ u-∇ ⋅ (u ∇ v)+ λ u-μ u^ κ,\0= Δ v-v+ u,.\qquad\qquad (⋆) ut …

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 …

The coupled chemotaxis–fluid system\left {&n_t+ u ⋅ ∇ n= Δ n-∇ ⋅ (n ∇ c)+ rn-μ n^ 2,\&
c_t+ u ⋅ ∇ c= Δ c-c+ n,\& u_t+ ∇ P= Δ u+ n ∇ ϕ+ g (x, t),\& ∇ ⋅ u= 0,. nt+ u·∇ n= Δ n …

The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes
equations through transport and buoyancy. It is shown that when posed with no-flux/no …