Displaying similar documents to “Existence of three solutions for a Navier boundary value problem involving the p(x)-biharmonic operator”

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

Chérif Amrouche, Patrick Penel, Nour Seloula (2013)

Annales mathématiques Blaise Pascal

Similarity:

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.

On a steady flow in a three-dimensional infinite pipe

Paweł Konieczny (2006)

Colloquium Mathematicae

Similarity:

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.

On the Navier-Stokes equations with anisotropic wall slip conditions

Christiaan Le Roux (2023)

Applications of Mathematics

Similarity:

This article deals with the solvability of the boundary-value problem for the Navier-Stokes equations with a direction-dependent Navier type slip boundary condition in a bounded domain. Such problems arise when steady flows of fluids in domains with rough boundaries are approximated as flows in domains with smooth boundaries. It is proved by means of the Galerkin method that the boundary-value problem has a unique weak solution when the body force and the variability of the surface friction...

Well-posedness issues for the Prandtl boundary layer equations

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

Séminaire Laurent Schwartz — EDP et applications

Similarity:

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.

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

Piotr Bogusław Mucha (2005)

Banach Center Publications

Similarity:

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.

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

Jan Prüss, Gieri Simonett (2009)

Banach Center Publications

Similarity:

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.