相关论文: On a regularized family of models for homogeneous …
We consider a general family of regularized systems for the full Ericksen-Leslie model for the hydrodynamics of liquid crystals in $n$-dimensional compact Riemannian manifolds, $n$=2,3. The system we consider consists of a regularized…
We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n greater than or equal to 2. This family captures most of…
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions…
We study a quasi-incompressible Navier--Stokes/Cahn--Hilliard coupled system which describes the motion of two macroscopically immiscible incompressible viscous fluids with partial mixing in a small interfacial region and long-range…
This paper studies two well-known models for two-phase fluid flow at constant temperature, the isothermal Navier-Stokes-Allen-Cahn and the isothermal Navier-Stokes-Cahn-Hilliard equations, both of which consist of equations for the (total)…
We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the…
We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in $\mathbb{R}^N$, and the Navier-Stokes-Korteweg equations is…
Over the past few decades, numerous N-phase incompressible diffuse-interface flow models with non-matching densities have been proposed. Despite aiming to describe the same physics, these models are generally distinct, and an overarching…
We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
In this work, we study the so-called Allen-Cahn-Navier-Stokes equations, a diffuse-interface model for two-phase incompressible flows with different densities. We first prove the local-in-time existence and uniqueness of classical solutions…
We investigate parameteric Navier-Stokes equations for a viscous, incompressible flow in bounded domains. The coefficients of the equations are perturbed by high-dimensional random parameters, this fits in particular for modelling flows in…
This work presents a macroscopic model for the flow of two immiscible and incompressible fluids within inhomogeneous porous media. At the pore scale, the flow is governed by the full Navier-Stokes equations while the phase interface…
This study establishes the global well-posedness of the compressible non-isentropic Navier-Stokes/Allen-Cahn system governed by the van der Waals equation of state $p(\rho,\theta)=- a\rho^2+\frac{R\theta\rho}{1-b\rho}$ and degenerate…
This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…
The compressible Navier-Stokes-Allen-Cahn system models the motion of a mixture of two macroscopically immiscible viscous compressible fluids. In this paper, we are concerned with the large time behavior of solutions to the Cauchy problem…
This paper studies the two-dimensional inhomogeneous Navier--Stokes equations governing stratified flows in a bounded domain under a gravitational potential \(f\). Our main results are as follows. First, we provide a rigorous…
This paper is devoted to the global well-posedness of two Diffuse Interface systems modeling the motion of an incompressible two-phase fluid mixture in presence of capillarity effects in a bounded smooth domain $\Omega\subset \mathbb{R}^d$,…
In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid…