Displaying similar documents to “Well-posedness issues for the Prandtl boundary layer equations”

Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations

Chérif Amrouche, Patrick Penel, Nour Seloula (2013)

Annales mathématiques Blaise Pascal

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This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.

Boundary conditions on artificial frontiers for incompressible and compressible Navier-Stokes equations

Charles-Henri Bruneau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Non reflecting boundary conditions on artificial frontiers of the domain are proposed for both incompressible and compressible Navier-Stokes equations. For incompressible flows, the boundary conditions lead to a well-posed problem, convey properly the vortices without any reflections on the artificial limits and allow to compute turbulent flows at high Reynolds numbers. For compressible flows, the boundary conditions convey properly the vortices without any reflections on the artificial...

On a steady flow in a three-dimensional infinite pipe

Paweł Konieczny (2006)

Colloquium Mathematicae

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The paper examines the steady Navier-Stokes equations in a three-dimensional infinite pipe with mixed boundary conditions (Dirichlet and slip boundary conditions). The velocity of the fluid is assumed to be constant at infinity. The main results show the existence of weak solutions with no restriction on smallness of the flux vector and boundary conditions.

New Wall Laws for the Unsteady Incompressible Navier-Stokes Equations on Rough Domains

Gabriel R. Barrenechea, Patrick Le Tallec, Frédéric Valentin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Different effective boundary conditions or wall laws for unsteady incompressible Navier-Stokes equations over rough domains are derived in the laminar setting. First and second order unsteady wall laws are proposed using two scale asymptotic expansion techniques. The roughness elements are supposed to be periodic and the influence of the rough boundary is incorporated through constitutive constants. These constants are obtained by solving steady Stokes problems and so they are...

Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension

Jan Prüss, Gieri Simonett (2009)

Banach Center Publications

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The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.

The Eulerian limit and the slip boundary conditions-admissible irregularity of the boundary

Piotr Bogusław Mucha (2005)

Banach Center Publications

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We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.