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 …

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 …

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 …

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 …

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 …

In this paper, we investigate the Cauchy problem for the two-dimensional incompressible
chemotaxis-Navier-Stokes equations. By taking advantage of a coupling structure of the …

In this paper we continue to deal with the initial–boundary value problem for the coupled
Keller–Segel–Stokes system {n t+ u⋅∇ n= Δ n−∇⋅(n S (x, n, c)⋅∇ c),(x, t)∈ Ω×(0, T), c t+ …

Abstract We consider the Keller–Segel system coupled with the Navier–Stokes fluid in the
whole space, and prove the existence of global mild solutions with the small initial data in …

Chemotaxis plays a crucial role in a variety of processes in biology and ecology. In many
instances, processes involving chemical attraction take place in fluids. One of the most …

We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-
Stokes equation n< sub> t+ u⋅∇ n= Δn-χ∇⋅(n∇ c), c< sub> t+ u⋅∇ c= Δc-nc, u< sub> t+ κ …