Related papers: Singular sensitivity in a Keller-Segel-fluid syste…

This paper is concerned with the following quasilinear chemotaxis--Navier--Stokes system with nonlinear diffusion and rotation $$ \left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(nS(x,n,c)\cdot\nabla c),\quad x\in \Omega,…

In this work, we study a chemotaxis-Navier-Stokes model in a two-dimensional setting as below, \begin{eqnarray} \left\{ \begin{array}{llll} \displaystyle n_{t}+\mathbf{u}\cdot\nabla n=\Delta n-\nabla \cdot(n\nabla c)+f(n),…

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg. By means of a partial regularity theorem (proved elsewhere), it turns out that we are…

In this paper, we study the nonconstant positive steady states of a Keller-Segel chemotaxis system over a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq 1$. The sensitivity function is chosen to be $\phi(v)=\ln (v+c)$ where $c$ is a…

In this paper, we consider the following system $$\left\{\begin{array}{ll} n_t+u\cdot\nabla n&=\Delta n-\nabla\cdot(n\mathcal{S}(|\nabla c|^2)\nabla c)-nm,\\ c_t+u\cdot\nabla c&=\Delta c-c+m,\\ m_t+u\cdot\nabla m&=\Delta m-mn,\\ u_t&=\Delta…

We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…

In this work we consider the Keller-Segel system coupled with Navier-Stokes equations in $\mathbb{R}^{N}$ for $N\geq2$. We prove the global well-posedness with small initial data in Besov-Morrey spaces. Our initial data class extends…

Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $\begin{equation} \begin{cases} u_{t} =\Delta u - \nabla \cdot(u \nabla v) \ \ \ \text{in } \mathbb{R}^2\times(0,T),\\[5pt] v =…

In present paper, we consider a chemotaxis consumption system with density-signal governed sensitivity and logistic source: $u_t=\Delta u-\nabla\cdot(\frac{S(u)}{v}\nabla v)+ru-\mu u^2$, $v_t=\Delta v-uv$ in a smooth bounded domain…

In this paper, we are concerned with a class of parabolic-elliptic chemotaxis systems encompassing the prototype $$\left\{\begin{array}{lll} &u_t = \nabla\cdot(\nabla u-\chi u\nabla v)+f(u), & x\in \Omega, t>0, \\[0.2cm] &0= \Delta v…

This paper considers the Keller-Segel model coupled to stochastic Navier-Stokes equations (KS-SNS, for short), which describes the dynamics of oxygen and bacteria densities evolving within a stochastically forced 2D incompressible viscous…

This paper is concerned with the Keller--Segel system with flux limitation, \begin{align} \tag{$\ast$} \begin{cases} u_t=\Delta u - \nabla \cdot (uf(|\nabla v|^{2})\nabla v), \\ v_t=\Delta v - v + u \end{cases} \end{align} in bounded…

This paper deals with the following quasilinear Keller-Segel-Navier-Stokes system modeling coral fertilization $(*)$: $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c)-nm,\quad x\in \Omega, t>0,…

This paper deals with the higher dimension quasilinear parabolic-parabolic Keller-Segel system involving a source term of logistic type $ u_t=\nabla\cdot(\phi(u)\nabla u)-\chi\nabla\cdot(u\nabla v)+g(u)$, $\tau v_t=\Delta v-v+u$ in…

This work studies the chemotaxis-haptotaxis system $$\left\{ \begin{array}{ll} u_t= \Delta u - \chi \nabla \cdot (u\nabla v) - \xi \nabla \cdot (u\nabla w) + \mu u(1-u-w), &\qquad x\in \Omega, \, t>0, \\[1mm] v_t=\Delta v-v+u, &\qquad x\in…

In my PhD thesis I show the existence of global-in-time weak solutions for a Navier-Stokes fluid interacting with a linearly elastic shell of Koiter type. This is achieved by the introduction of a new method for showing the compactness of…

This paper is concerned with the uniqueness of solutions to the following nonlocal semi-linear elliptic equation \begin{equation}\label{ellip}\tag{$\ast$} \Delta u-\beta u+\lambda\frac{e^u}{\int_{\Omega}e^u}=0~\mathrm{in}~\Omega,…

We establish criteria on the chemotactic sensitivity $\chi$ for the non-existence of global weak solutions (i.e. \textit{blow-up} in finite time) to a stochastic Keller--Segel model with spatially inhomogeneous, conservative noise on…

In this paper, we deal with quasilinear Keller--Segel systems with indirect signal production, $$\begin{cases} u_t = \nabla \cdot ((u+1)^{m-1}\nabla u) - \nabla \cdot (u \nabla v), &x \in \Omega,\ t> 0,\\ 0 = \Delta v - \mu(t) + w, &x \in…

The chemotaxis-Navier-Stokes system \begin{equation*}\label{1} \left\{ \begin{array}{rcl} n_t+u\cdot\nabla n &=& \Delta \big(n c^{-\alpha} \big), \\[1mm] c_t+ u\cdot\nabla c &=& \Delta c -nc,\\[1mm] u_t + (u\cdot\nabla) u &=&\Delta u+\nabla…