相关论文: Generalized solutions to a chemotaxis-Navier-Stoke…

The present paper aims at the investigation of the global stability of large solutions to the compressible Navier-Stokes equations in the whole space. Our main results and innovations can be concluded as follows: Under the assumption that…

The linear Navier-Stokes equations in three dimensions are given by: $u_{it}(x,t)-\rho \triangle u_i(x,t)-p_{x_i}(x,t)=$ $w_i(x,t)$ , $div \textbf{u}(x,t)=0,i=1,2,3$ with initial conditions: $\textbf{u}|_{(t=0)\bigcup\partial\Omega}=0$. The…

This paper deals with the problem of global solvability and boundedness of classical solutions to a fully parabolic chemotaxis system with singular sensitivity in any dimensional setting. In particular, We show that the system…

This paper is concerned with a quasilinear chemotaxis model with indirect signal production, $u_t = \nabla\cdot(D(u)\nabla u - S(u)\nabla v)$, $v_t = \Delta v - v + w$ and $w_t = \Delta w - w + u$, posed on a bounded smooth domain…

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an…

A sufficient condition of regularity for solutions to the Navier-Stokes equations is proved. It generalizes the so-called $L_{3,\infty}$-case.

We show that solutions $u(x,t)$ of the non-stationnary incompressible Navier--Stokes system in $\R^d$ ($d\geq2$) starting from mild decaying data $a$ behave as $|x|\to\infty$ as a potential field: u(x,t) = e^{t\Delta}a(x) +…

This paper investigates the following quasilinear Keller-Segel-Navier-Stokes system $$\left\{ \begin{array}{l} n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\nabla c),\quad x\in \Omega, t>0, \\ c_t+u\cdot\nabla c=\Delta c-c+n,\quad x\in…

For the physically important case in which the viscosity coefficients depend on the density $\rho$ through a power law (i.e., $\rho^\delta$ with some exponent $\delta \in (\frac{1}{2},1)$), we establish the global well-posedness of regular…

In this article, we study the solutions of the damped Navier--Stokes equation with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$ with smooth boundary. The existence of the solutions is global with the damped term…

In this paper, we simplify and extend the results of \cite{GZ} to include the case in which $\Om =\R^3$. Let ${[L^2({\mathbb{R}}^3)]^3}$ be the Hilbert space of square integrable functions on ${\mathbb {R}}^3 $ and let ${\mathbb…

We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume…

Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been…

Systems of the type $$\begin{cases} u_t = \nabla \cdot (D_1(u) \nabla u - S_1(u) \nabla v) + f_1(u, v),\\ v_t = \nabla \cdot (D_2(v) \nabla v + S_2(v) \nabla u) + f_2(u, v) \end{cases} \qquad (\star)$$ can be used to model pursuit-evasion…

A fundamental problem in analysis is to decide whether a smooth solution exists for the Navier-Stokes equations in three dimensions. In this paper we shall study this problem. The Navier-Stokes equations are given by:…

We consider the chemotaxis-fluid system \begin{align}\label{star}\tag{$\diamondsuit$} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\quad}l@{\,}c} n_{t}&+&u\cdot\!\nabla n&=\Delta n^m-\nabla\!\cdot(n\nabla c),\ &x\in\Omega,& t>0,\\…

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…

In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tamed Navier-Stokes equations (STCNS, for short). Our main goal…

We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…

We consider the Cauchy problem in the band $\mathbb{C}^{n}\times[0, T], n>1,T>0$, for a system of nonlinear differential equations structurally similar to the classical Navier-Stokes equations for an incompressible fluid. The main…