ﻻ يوجد ملخص باللغة العربية
The chemotaxis--Navier--Stokes system begin{equation*}label{0.1} left{begin{array}{ll} n_t+ucdot abla n=triangle n-chi ablacdotp left(displaystylefrac n {c} abla cright)+n(r-mu n), c_t+ucdot abla c=triangle c-nc, u_t+ (ucdot abla) u=Delta u+ abla P+n ablaphi, ablacdot u=0, end{array}right. end{equation*} is considered in a bounded smooth domain $Omega subset mathbb{R}^2$, where $phiin W^{1,infty}(Omega)$, $chi>0$, $rin mathbb{R}$ and $mu> 0$ are given parameters. It is shown that there exists a value $mu_*(Omega,chi, r)geq 0$ such that whenever $ mu>mu_*(Omega,chi, r)$, the global-in-time classical solution to the system is uniformly bounded with respect to $xin Omega$. Moreover, for the case $r>0$, $(n,c,frac {| abla c|}c,u)$ converges to $(frac r mu,0,0,0)$ in $L^infty(Omega)times L^infty(Omega)times L^p(Omega)times L^infty(Omega)$ for any $p>1$ exponentially as $trightarrow infty$, while in the case $r=0$, $(n,c,frac {| abla c|}c,u)$ converges to $(0,0,0,0)$ in $(L^infty(Omega))^4$ algebraically. To the best of our knowledge, these results provide the first precise information on the asymptotic profile of solutions in two dimensions.
This paper investigates an incompressible chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion begin{eqnarray} left{begin{array}{lll} n_t+ucdot abla n= ablacdot(| abla n|^{p-2} abla n)- ablacdot(nchi(c) abla c),& xinOmega, t>0, c_t+ucdot
In this paper, the existence and uniqueness of strong axisymmetric solutions with large flux for the steady Navier-Stokes system in a pipe are established even when the external force is also suitably large in $L^2$. Furthermore, the exponential conv
This paper deals with a boundary-value problem in three-dimensional smooth bounded convex domains for the coupled chemotaxis-Stokes system with slow $p$-Laplacian diffusion begin{equation} onumber left{ begin{aligned} &n_t+ucdot abla n= ablacdo
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard Cahn-Hilliard equati
This paper is concerned with traveling wave solutions of the following full parabolic Keller-Segel chemotaxis system with logistic source, begin{equation} begin{cases} u_t=Delta u -chi ablacdot(u abla v)+u(a-bu),quad xinmathbb{R}^N cr tau v_t=Delta v