Related papers: A Banach space formulation for the fully dynamic N…
In this dissertation two-dimensional buoyancy-driven flows are investigated. While usually the Navier-Stokes equations are equipped with no-slip boundary conditions here we focus on the Navier-slip conditions that, depending on the system…
We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…
In this paper, we investigate the incompressible steady Navier-Stokes system with Navier slip boundary condition in a two-dimensional channel. As long as the width of cross-section of the channel grows more slowly than the linear growth,…
From a unified vision of vector valued solutions in weighted Banach spaces, this manuscript establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex…
We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…
In this paper, we propose and analyze a mixed formulation for the Kelvin-Voigt-Brinkman-Forchheimer equations for unsteady viscoelastic flows in porous media. Besides the velocity and pressure, our approach introduces the vorticity as a…
We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by…
We investigate the limiting behavior of the Navier-Stokes-Cahn-Hilliard model for binary-fluid flows as the diffuse-interface thickness passes to zero, in the presence of fluid-fluid-solid contact lines. Allowing for motion of such contact…
We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…
We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…
In this paper we are concerned with the initial boundary value problem of the 2, 3-D Navier-Stokes equations with mixed boundary conditions including conditions for velocity, static pressure, stress, rotation and Navier slip condition…
The Navier--Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the…
In this paper, we analyze the Nitsche's method for the stationary Navier-Stokes equations on Lipschitz domains under minimal regularity assumptions. Our analysis provides a robust formulation for implementing slip (i.e. Navier) boundary…
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…
The volume-filtering of the Navier-Stokes equations allows to consider the effect that particles have on the fluid without further assumptions, but closures arise of which the implications are not fully understood. In the present paper, we…
Modeling and simulation of fluid-structure interactions are crucial to the success of aerospace engineering. This work addresses a novel hybrid algorithm that models the close coupling between compressible flows and deformable materials…
A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…
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…
The Navier-Stokes equations describe the motion of viscous fluids. In order to predict turbulent flows with reasonable computational time and accuracy, these equations are spatially filtered according to the large-eddy simulation (LES)…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…