Related papers: Global boundedness and absorbing sets in two-dimen…
We consider a parabolic-elliptic Keller-Segel system with spatially dependent diffusion sensitivity \begin{eqnarray*} \left\{ \begin{array}{l} u_t = \nabla \cdot (|x|^\beta \nabla u) - \nabla \cdot (u\nabla v), \\[1mm] 0 = \Delta v - \mu +…
We study a thermodynamically consistent diffuse interface model that describes the motion of a two-phase flow of two viscous incompressible Newtonian fluids with unmatched densities and a soluble surfactant in a bounded domain of two or…
In this paper, we consider the following parabolic-parabolic-elliptic system } \begin{align*} \left\{\aligned & u_t=\Delta u-\nabla\cdot(u\nabla v)+\xi\nabla\cdot(u\nabla w)+au-\mu u^{\alpha}, && x\in\Omega, t>0,\\ & v_t=\Delta…
We consider a chemotaxis-fluid system in the whole plane $\mathbb{R}^{2}$ which describes the motion of bacteria suspended in a Navier-Stokes fluid and attracted by a chemical (oxygen). Employing the vorticity formulation for the fluid…
The basic chemotaxis-consumption model \[ u_t = \Delta u - \nabla \cdot(u\nabla v),\qquad\qquad v_t = \Delta v - uv \] is considered in general, possibly non-convex bounded domains of arbitrary spatial dimension. Global existence of weak…
This work deals with a fully parabolic chemotaxis model with nonlinear production and chemoattractant. The problem is formulated on a bounded domain and, depending on a specific interplay between the coefficients associated to such…
This paper investigates a {{three-component}} chemotaxis system involving both attraction and repulsion effects, as well as a nonlocal logistic-type source term. Mathematically, if $u=u(x,t)$, $v = v(x,t)$ and $w = w(x,t)$ denote the cell…
In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for a two-species chemotaxis consumption model in a bounded smooth but not necessarily convex domain $\Omega\subset \mathbb{R}^n…
This paper deals with the Neumann boundary value problem for the system $$u_t=\nabla\cdot\left(D(u)\nabla u\right)-\nabla\cdot\left(S(u)\nabla v\right)+f(u) ,\quad x\in\Omega,\ t>0$$ $$v_t=\Delta v-v+u,\quad x\in\Omega,\ t>0$$ in a smooth…
A chemotaxis system possibly containing rotational components of the cross-diffusive flux is studied under no-flux boundary conditions in a bounded domain $\Omega\subset R^n$, $n\ge 1$, with smooth boundary, where the evolution of the…
In this paper, we investigate a chemotaxis-fluid system involving both the effect of potential force on cells and the effect of chemotactic force on fluid: \begin{equation*} \left\{ \begin{split} \partial_t n + \mathbf{u}\cdot\nabla n & =…
In recent years, a lot of attention has been drawn to the question of whether logistic kinetics is sufficient to enforce the global existence of classical solutions or to prevent finite-time blow-up in various chemotaxis models. The current…
This paper is concerned with the global well-posedness of a chemotaxis-Euler system in bounded domains of $\mathbb{R}^2$. Completing the system with physical boundary conditions, we show that the corresponding initial boundary value problem…
The present work deals with a Keller-Segel-Navier-Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and of Dirichlet type for the velocity field, over a bounded…
This paper is concerned with radially symmetric solutions of the parabolic-elliptic version of the Keller-Segel system with flux limitation, as given by \begin{equation} \left\{ \begin{array}{l} \displaystyle u_t=\nabla \cdot…
This paper investigates the following chemotaxis system featuring weak degradation and nonlinear motility functions \begin{equation}\label{Model1} \begin{cases} u_{t} = (\gamma(v)u)_{xx} + r - \mu u, & x \in [0,L],\ t > 0, v_{t} = v_{xx} -…
This paper is concerned with the doubly degenerate nutrient taxis system $u_t=\nabla \cdot(u^{l-1} v \nabla u)- \nabla \cdot\left(u^{l} v \nabla v\right)+ uv$ and $v_t=\Delta v-u v$ for some $l \geqslant 1$, subjected to homogeneous Neumann…
In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier-Stokes system with vacuum in a bounded domain $\Omega\subset \mathbb{R}^3$ by the bootstrap argument provided that the…
We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…
This paper is concerned with different logistic damping effects on the global existence in a chemotaxis system \begin{equation*} \left\{\aligned & u_{t}=\Delta u-\chi_{1}\nabla\cdot(u\nabla w)+w-\mu_{1}u^{r_{1}},&&x\in\Omega,t>0, &…