Related papers: Global existence for an attraction-repulsion chemo…
We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…
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 prove the local well-posedness for the barotropic compressible Navier-Stokes system on a moving domain, a motion of which is determined by a given vector field ${\bf V}$, in a maximal $L_p-L_q$ regularity framework. Under additional…
We consider the barotropic Navier--Stokes system describing the motion of a viscous compressible fluid interacting with the outer world through general in/out flux boundary conditions. We consider a hard--sphere type pressure EOS and show…
The micropolar equations are a useful generalization of the classical Navier-Stokes model for fluids with micro-structure. We prove the existence of global and strong solutions to these equations in cylindrical domains in $\mathbb{R}^3$. We…
This work is concerned with the global existence of large solutions to the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible…
We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law and prove a global…
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the motion of the rigid body is described by the…
In this work, we study global existence, eventual smoothness and asymptotical behavior of positive solutions for a two-species chemotaxis consumption model in a bounded smooth but not necessarily convex domain $\Omega\subset \mathbb{R}^n…
We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We consider two cases, depending on the values of the parameters…
In this paper, we consider the following attraction repulsion chemotaxis model with nonlinear signal term: \begin{align*} &u_{t}=\nabla \cdot(\nabla u-\xi_{1} u \nabla v +\xi_{2} u \nabla w), \quad &0=\Delta v -\lambda_{1}v +f_{1}(u), \quad…
This paper presents a rigorous derivation of an effective model for fluid flow through a thin elastic porous membrane separating two fluid bulk domains. The microscopic setting involves a periodically structured porous membrane composed of…
We consider the compressible Navier-Stokes system where the viscosity depends on density and the heat conductivity is proportional to a positive power of the temperature under stress-free and thermally insulated boundary conditions. Under…
A model of fully developed turbulence of a compressible fluid is briefly reviewed. It is assumed that fluid dynamics is governed by a stochastic version of Navier-Stokes equation. We show how corresponding field theoretic-model can be…
This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…
In this paper, we investigate the long-time dynamics of a repulsive Keller-Segel chemotaxis system. The model features negative chemotaxis, logistic growth and a cell death term, accounting for a lethal chemorepellent that is self-produced…
A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic…
In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…
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}\nonumber \left\{ \begin{aligned} &n_t+u\cdot\nabla…