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We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…
In this paper, we study a nonlinear fluid-structure interaction problem driven by a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D…
In this article, we study boundary null controllability properties of the linearized compressible Navier-Stokes equations in the interval $(0,2\pi)$ for both barotropic and non-barotropic fluids using only one boundary control. We consider…
The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes equations (CHNS System). In this work, we study the well-posedness results for the CHNS system with…
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in…
We introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation $\{{\cal T}_h \}_{h>0}$. The eddy viscosity is expressed…
The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…
This paper is concerned with a diffuse interface model called as Navier-Stokes/Cahn-Hilliard system. This model is usually used to describe the motion of immiscible two-phase flow with diffusion interface. For the periodic boundary value…
Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…
We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…
We consider optimal control problems of systems governed by stationary, incompressible generalized Navier-Stokes equations with shear dependent viscosity in a two-dimensional or three-dimensional domain. We study a general class of…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
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…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
The evolution of two partially miscible, nonhomogeneous, incompressible viscous fluids of non-Newtonian type, can be governed by the Navier-Stokes-Cahn-Hilliard system. In the present work, we prove the global existence of weak solutions…
In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell…
We show that molecular dynamics simulations can furnish useful boundary conditions at a solid surface bounding a two-component fluid. In contrast to some previous reports, convective-diffusive flow is consistent with continuum equations…
We present a novel partitioned iterative formulation for modeling of fluid-structure interaction in two-phase flows. The variational formulation consists of a stable and robust integration of three blocks of differential equations, viz.,…
We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velocity boundary conditions, this leads to a coupled system of…
We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…