Displaying similar documents to “Some Remarks on the Boundary Conditions in the Theory of Navier-Stokes Equations”

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.

The Stokes system in the incompressible case-revisited

Rainer Picard (2008)

Banach Center Publications

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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.

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.

Well-posedness issues for the Prandtl boundary layer equations

David Gérard-Varet, Nader Masmoudi (2013-2014)

Séminaire Laurent Schwartz — EDP et applications

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These notes are an introduction to the recent paper [7], about the well-posedness of the Prandtl equation. The difficulties and main ideas of the paper are described on a simpler linearized model.