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This paper concerns the global existence for classical solutions problem to the 3D Density-Dependent Viscosity barotropic compressible Navier-Stokes in $\Omega$ with slip boundary condition, where $\Omega$ is a simply connected bounded…

This paper studies the chemotaxis-haptotaxis system \begin{equation}\nonumber \left\{ \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot(u\nabla v)-\xi\nabla\cdot(u\nabla w)+\mu u(1-u-w), &(x,t)\in \Omega\times (0,T),\\ v_t=\Delta v-v+u,…

We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system with smooth initial data which are of small energy but possibly large oscillations where the initial…

The chemotaxis system \begin{align*} u_t &= \Delta u - \nabla \cdot (u\nabla v), \\ v_t &= \Delta v - uv, \end{align*} is considered under the boundary conditions $\frac{\partial u}{\partial\nu}- u\frac{\partial v}{\partial\nu}=0$ and…

This paper considers the chemotaxis-Navier--Stokes system with nonlinear diffusion and logistic-type degradation term \begin{align*} \begin{cases} n_t + u\cdot\nabla n = \nabla \cdot(D(n)\nabla n) - \nabla\cdot(n \chi(c) \nabla c) + \kappa…

We consider the spatially $3$-D version of the following Keller-Segel-Navier-Stokes system with rotational flux $$\left\{\begin{array}{l} n_t+u\cdot\nabla n=\Delta n-\nabla\cdot(nS(x,n,c)\nabla c),\quad x\in \Omega, t>0, c_t+u\cdot\nabla…

We consider initial-boundary value problems for the $\kappa$-dependent family of chemotaxis-(Navier--)Stokes systems \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=\Delta…

In this paper, we investigate the existence of a global classical solution to 3D Cauchy problem of the isentropic compressible Navier-Stokes equations with large initial data and vacuum. Precisely, when the far-field density is vacuum…

In this paper, we investigate the global solvability of the chemotaxis-Navier-Stokes system on a three-dimensional moving domain of finite depth, bounded below by a rigid flat bottom and bounded above by the free surface. Completing 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 & =…

This paper considers the dynamics of the following chemotaxis system $$ \begin{cases} u_t=\Delta u-\chi\nabla (u\cdot \nabla v)+u\left(a_0(t,x)-a_1(t,x)u-a_2(t,x)\int_{\Omega}u\right),\quad x\in \Omega\cr 0=\Delta v+ u-v,\quad x\in \Omega…

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…

For periodic initial data with initial density, we establish the global existence and uniqueness of strong and classical solutions for the two-dimensional compressible Navier-Stokes equations with no restrictions on the size of initial data…

We consider a chemotaxis-Navier-Stokes system modelling cellular swimming in fluid drops where an exchange of oxygen between the drop and its environment is taken into account. This phenomenon results in an inhomogeneous Robin-type boundary…

We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \begin{align*} \left\{ \begin{array}{c@{\quad}l@{\quad}l@{\,}c} n_{t}+u\cdot\nabla n=\nabla\cdot\big(D(n)\nabla n-nS(x,n,c)\cdot\nabla c\big),\…

This paper deals with classical solutions to the parabolic-parabolic system \begin{align*} \begin{cases} u_t=\Delta (\gamma (v) u ) &\mathrm{in}\ \Omega\times(0,\infty), \\[1mm] v_t=\Delta v - v + u &\mathrm{in}\ \Omega\times(0,\infty),…

For smooth initial data, we establish the global existence and uniqueness of strong and classical solutions to the Cauchy problem for the barotropic compressible Navier-Stokes equations in two spatial dimensions with vacuum state as far…

In this paper, the fully parabolic Keller-Segel system \begin{equation} \left\{ \begin{array}{llc} u_t=\Delta u-\nabla\cdot(u\nabla v), &(x,t)\in \Omega\times (0,T),\\ v_t=\Delta v-v+u, &(x,t)\in\Omega\times (0,T),\\ \end{array} \right.…

We consider the parabolic-elliptic Keller-Segel system \[ \left\{ \begin{aligned} u_t &= \Delta u - \chi \nabla \cdot (u \nabla v), \\ 0 &= \Delta v - v + u \end{aligned} \right. \tag{$\star$} \] in a smooth bounded domain $\Omega \subseteq…

Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*} n_t &= \Delta n - \nabla \cdot (n \nabla c), \\ 0 &= \Delta c - nc, \end{align*} under no-flux boundary conditions for $n$ and…