The stationary exterior 3 D-problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces.
The Stokes system in the incompressible case-revisited
The classical Stokes system is reconsidered and reformulated in a functional analytical setting allowing for low regularity of the data and the boundary. In fact the underlying domain can be any non-empty open subset Ω of ℝ³. A suitable solution concept and a corresponding solution theory is developed.
The Tartar equation for homogenization of a model of the dynamics of fine-dispersion mixtures.
The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation
We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications...
Time-dependent Stokes equations with measure data.
Towards robust 3D -pinch simulations: Discretization and fast solvers for magnetic diffusion in heterogeneous conductors.
Tuning the mesh of a mixed method for the stream function. Vorticity formulation of the Navier-Stokes equations.
Two-level stabilized nonconforming finite element method for the Stokes equations
In this article, we present a new two-level stabilized nonconforming finite elements method for the two dimensional Stokes problem. This method is based on a local Gauss integration technique and the mixed nonconforming finite element of the pair (nonconforming linear element for the velocity, conforming linear element for the pressure). The two-level stabilized finite element method involves solving a small stabilized Stokes problem on a coarse mesh with mesh size and a large stabilized Stokes...
Uniformly stable mixed hp-finite elements on multilevel adaptive grids with hanging nodes
We consider a family of quadrilateral or hexahedral mixed hp-finite elements for an incompressible flow problem with Qr-elements for the velocity and discontinuous -elements for the pressure where the order r can vary from element to element between 2 and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.
Weighted L² and approaches to fluid flow past a rotating body
Consider the flow of a viscous, incompressible fluid past a rotating obstacle with velocity at infinity parallel to the axis of rotation. After a coordinate transform in order to reduce the problem to a Navier-Stokes system on a fixed exterior domain and a subsequent linearization we are led to a modified Oseen system with two additional terms one of which is not subordinate to the Laplacean. In this paper we describe two different approaches to this problem in the whole space case. One of them...
К теории устойчивости решений полулинейных диссипативных уравнений типа С.Л.Соболева
О некоторых задачах векторного анализа и обобщенных постановках краевых задач для уравнений Навье-Стокса
Об одном классе кривых, возникающем в задаче со свободной границей для течений Стокса.
Об операторе линеаризованной стационарной задачи Навье-Стокса
Об операторной трактовке стокслета.
Об оценке решений системы Стокса во внешних областях
Обобщенные решения с первыми производными из в задаче обтекания для системы Стокса.
Разрешимость одной модельной задачи для уравнений Стокса в бесконечном угле
Решение стационарной задачи обтекания в постановке Стокса в пространствах .
Три задачи теории сплошных сред в многогранниках