Related papers: A chemotaxis-Navier-Stokes system with dynamical b…
In this paper we study the Navier-Stokes equations with a Navier-type boundary condition that has been proposed as an alternative to common near wall models. The boundary condition we study, involving a linear relation between the…
We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…
We consider the viscous incompressible fluids in a three-dimensional horizontally periodic domain bounded below by a fixed smooth boundary and above by a free moving surface. The fluid dynamics are governed by the Navier-Stokes equations…
In this paper we consider evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under Rauch…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
In this paper we consider the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces $X$ and $Y$, respectively, to be the…
We consider the Navier-Stokes-Fourier system with the inhomogeneous boundary conditions for the velocity and the temperature. We show that solutions emanating from sufficiently regular data remain regular as long as the density $\varrho$,…
We study the barotropic compressible Navier-Stokes equations with Navier-type boundary condition in a two-dimensional simply connected bounded domain with $C^{\infty}$ boundary $\partial\Omega.$ By some new estimates on the boundary related…
We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2d…
In this paper we consider a coupled hydrodynamical system which involves the Navier-Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. By applying the Chemin-Lerner's time-space…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
We consider the stationary Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under the slip boundary conditions. Our aim is to show that a solution to the bulk equations is approximated by a…
Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…
This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain,…
We show that if u is a weak solution to the Navier-Stokes initial-boundary value problem with Navier's slip boundary conditions in $Q_T:=\Omega\times(0,T)$, where $\Omega$ is a domain in $R^3$, then an associated pressure $p$ exists as a…
The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface, despite the assumption of the no-slip condition is preferred to avoid boundary terms in the analysis…
In this paper, we prove the existence and a partial regularity of a weak solution to the system governing the interaction between a rigid body and a viscous incompressible Newtonian fluid. The evolution of the system body-fluid is studied…
The dynamics defined by the Navier-Stokes equations under the Marangoni boundary conditions in a two dimensional domain is considered. This model of fluid dynamics involve fundamental physical effects: convection, diffusion and capillary…
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…
We study the Stokes system with the localized boundary data in the half-space. We are concerned with the local regularity of its solution near the boundary away from the support of the given boundary data which are product forms of each…