相关论文: Singular sensitivity in a Keller-Segel-fluid syste…
In this paper, we study isolated singular positive solutions for the following Kirchhoff--type Laplacian problem: \begin{equation*} -\left(\theta+\int_{\Omega} |\nabla u| dx\right)\Delta u =u^p \quad{\rm in}\quad \Omega\setminus…
Nonnegative solutions of the Neumann initial-boundary value problem for the chemotaxis system \begin{align}\label{prob:star}\tag{$\star$} \begin{cases} u_t = \Delta u - \nabla \cdot (u \nabla v) + \lambda u - \mu u^\kappa, \\\\ 0 = \Delta v…
In this paper we consider a coupled hydrodynamical system which involves the Navier-Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. By applying the Chemin-Lerner's time-space…
This paper deals with a hyperbolic Keller-Segel system of consumption type with the logarithmic sensitivity \begin{equation*} \partial_{t} \rho = - \chi\nabla \cdot \left (\rho \nabla \log c\right),\quad \partial_{t} c = - \mu c\rho\quad…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
Singularities of the Navier-Stokes equations occur when some derivative of the velocity field is infinite at any point of a field of flow (or, in an evolving flow, becomes infinite at any point within a finite time). Such singularities can…
This paper is concerned with the global existence and uniqueness of classical solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in three-dimensional bounded domains or in the whole space…
We consider a degenerate quasilinear chemotaxis--Stokes type involving rotation in the aggregative term, \begin{equation} \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, t>0,…
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 & =…
This paper is Part II of a series on global existence and asymptotic behavior of positive solutions to \begin{equation*} \begin{cases} \displaystyle u_t=\Delta u-\chi_0\nabla\cdot\left(\frac{u^m}{(1+v)^\beta}\nabla…
We prove the global well-posedness of the one-dimensional Navier-Stokes-Korteweg equations driven by a stochastic multiplicative noise. The analysis is performed for the general case of capillarity and viscosity coefficients $k(\rho)=…
The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…
We study the limit of the stochastic model for two dimensional second grade fluids subjected to the periodic boundary conditions as the stress modulus tends to zero. We show that under suitable conditions on the data the whole sequence of…
The Keller-Segel-Navier-Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial cell…
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…
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and…
This paper establishes the global uniform-in-time boundedness of solutions to the following Keller-Setel system with signal-dependent diffusion and chemotaxis \begin{equation}\left\{ \begin{array}{ll} u_t=\nabla\cdot(\gamma(v)\nabla u -…
This paper examines the uniqueness/non-uniqueness of local-in-time strong solutions for the incompressible 3D Navier-Stokes equations in bounded domains, which are $\partial_t u=\nu \Delta u- u\cdot \nabla u-\nabla p+ f$ and $div~u=0$. The…
We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis-Navier-Stokes system in a smooth bounded domain $\Omega\subset\mathbb{R}^3$. It is shown that there exists a unique strong solution of the…