Related papers: On Cahn-Hilliard-Navier-Stokes equations with Nonh…
In this article, we study the solutions of the damped Navier--Stokes equation with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$ with smooth boundary. The existence of the solutions is global with the damped term…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
We study global existence and uniqueness of solutions to instationary inhomogeneous Navier-Stokes equations on bounded domains of $\R^n, n\geq 3$, with initial velocity in $B^0_{q,\infty}(\Om)$, $q\geq n$, and piecewise constant initial…
In this work, we study an optimal boundary control for the stochastic Allen Cahn Navier Stokes system. The governing system of nonlinear partial differential equations consists of the stochastic Navier Stokes equations with non homogeneous…
In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary condition and relaxation boundary condition in a channel, which is…
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…
The Cahn-Hilliard equation is the most common model to describe phase separation processes of a mixture of two components. For a better description of short-range interactions of the material with the solid wall, various dynamic boundary…
We consider the incompressible Euler and Navier-Stokes equations in a three-dimensional moving thin domain. Under the assumption that the moving thin domain degenerates into a two-dimensional moving closed surface as the width of the thin…
We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to…
We study a three-dimensional fluid-structure interaction problem describing the motion of an incompressible, viscous fluid coupled with a deformable elastic shell of Koiter type that forms part of the fluid boundary. The fluid motion is…
We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier-Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain $R^d (d = 2, 3)$, provided…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
The steady motion of a viscous incompressible fluid in a junction of unbounded channels with sources and sinks is modeled through the Navier-Stokes equations under inhomogeneous Dirichlet boundary conditions. In contrast to many previous…
We study the incompressible Navier-Stokes equations in the two-dimensional strip $\mathbb{R} \times [0,L]$, with periodic boundary conditions and no exterior forcing. If the initial velocity is bounded, we prove that the solution remains…
The initial-boundary value problem in a bounded domain with moving boundaries and nonhomogeneous boundary conditions for a higher order nonlinear Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global weak solutions…
This paper is mainly concerned with an initial-boundary value problem of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with the Landau potential in a two and three dimensions. The existence of strong solutions with…
We investigate the asymptotic behaviour of fast rotating incompressible fluids with vanishing viscosity, in a {three dimensional} domain with topography including the case of land area. Assuming the initial data is well-prepared, we prove a…
We prove the existence of a weak solution to the compressible Navier--Stokes system with singular pressure that explodes when density achieves its congestion level. This is a quantity whose initial value evolves according to the transport…
We study the nonhomogeneous boundary value problem for Navier--Stokes equations of steady motion of a viscous incompressible fluid in a two--dimensional bounded multiply connected domain $\Omega=\Omega_1\setminus\bar{\Omega}_2,…
We establish the global existence of a class of weak solutions to the isentropic compressible Navier-Stokes equations in a half-plane with Dirichlet boundary conditions, allowing for vacuum both in the interior and at infinity, under a…