Related papers: Uniqueness and regularity for the Navier-Stokes-Ca…
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier--Stokes system with a convective nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently proved…
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…
Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…
We consider a diffuse-interface model for two-phase incompressible viscous flows with a soluble surfactant in a bounded porous medium. This hydrodynamic system consists of a Darcy--Forchheimer equation for the seepage velocity…
We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation…
We study in this paper the movement of a rigid solid inside an incompressible Navier-Stokes flow, within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface, through a Navier condition. Taking into…
In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes…
In the well-known book of Lions [{\em Mathematical topics in fluid mechanics. Incompressible models}, 1996], global existence results of finite energy weak solutions of the inhomogeneous incompressible Navier-Stokes equations (INS) were…
In this paper, we investigate the uniform regularity for the isentropic compressible Navier-Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there…
We consider a diffuse interface model that describes the macro- and micro-phase separation processes of a polymer mixture. The resulting system consists of a Cahn-Hilliard equation and a Cahn-Hilliard-Oono type equation endowed with the…
A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…
This paper proves existence of a global weak solution to the inhomogeneous (i.e., non-constant density) incompressible Navier-Stokes system with mass diffusion. The system is well-known as the Kazhikhov-Smagulov model. The major novelty of…
We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…
Consider the Navier-Stokes flow in 3-dimensional exterior domains, where a rigid body is translating with prescribed translational velocity $-h(t)u_\infty$ with constant vector $u_\infty\in \mathbb R^3\setminus\{0\}$. Finn raised the…
We study the Cauchy problem for the isentropic hypo-viscous compressible Navier-Stokes equations (CNS) under general pressure laws in all dimensions $d\geq 2$. For all hypo-viscosities $(-\Delta)^\alpha$ with $\alpha\in (0,1)$, we prove…
This paper addresses the three-dimensional Navier-Stokes equations for an incompressible fluid whose density is permitted to be inhomogeneous. We establish a theorem of global existence and uniqueness of strong solutions for initial data…
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…
We study a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. Furnishing with classical no-slip, no-spin and no-flux boundary conditions, in a smooth and…
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…
We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…