Related papers: Capillarity driven Stokes flow: the one-phase prob…
We investigate theoretically on the basis of the steady Stokes equations for a viscous incompressible fluid the flow induced by a Stokeslet located on the centre axis of two coaxially positioned rigid disks. The Stokeslet is directed along…
The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…
We analytically derive an equation describing vesicle evolution in a fluid where some stationary flow is excited regarding that the vesicle shape is close to a sphere. A character of the evolution is governed by two dimensionless…
We consider the Stokes system in a thin porous medium $\Omega_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe…
Our aim is to analyse special type of boundary conditions, created to simulate flows like in cardiovascular and respiratory systems. Firstly, we will describe model of viscous, incompressible fluid in a domain consisting many inlets and…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…
Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…
This article is the first in a series of papers on the analysis of a basic model for fluid vesicle dynamics. There are two variants of this model, a parabolic one decribing purely relaxational dynamics and a non-parabolic one containing the…
We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…
In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the $\alpha$-viscosity parameter. This method reduces the problem of solving a…
In this work, we present observable consequences of parity-violating odd viscosity term in incompressible 2+1D hydrodynamics. For boundary conditions depending on the velocity field (flow) alone we show that: (i) The fluid flow quantified…
We establish the global well-posedness of the free boundary problem of the viscous pressureless and almost pressureless heat conductive flows in one space dimension. In both cases, arbitrarily large but smooth initial data is considered,…
We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our…
Lipid vesicles play a key role in fundamental biological processes. Despite recent progress, we lack a complete understanding of the non-equilibrium dynamics of vesicles due to challenges associated with long-time observation of shape…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…
We study an incompressible viscous flow around an obstacle with an oscillating boundary that moves by a translational periodic motion, and we show existence of strong time-periodic solutions for small data in different configurations: If…
In this paper, we proved the local well-posedness for the Navier-Stokes equtions describing the motion of isotropic barotoropic compressible viscous fluid flow with non-slip boundary conditions, wehre the fluid domain is the half-space in…
This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…