Displaying similar documents to “On some free boundary problems for Navier-Stokes equations”

Dimension reduction for incompressible pipe and open channel flow including friction

Ersoy, Mehmet

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We present the full derivation of a one-dimensional free surface pipe or open channel flow model including friction with non constant geometry. The free surface model is obtained from the three-dimensional incompressible Navier-Stokes equations under shallow water assumptions with prescribed "well-suited" boundary conditions.

Global free boundary problem for incompressible magnetohydrodynamics

Piotr Kacprzyk

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We consider the motion of incompressible mhd in a domain bounded a free surface. In the external domain there exists an electromagnetic field generated by some currents which keeps the mhd flow in the bounded domain. On the free surface transmission conditions for the electromagnetic fields are imposed. For sufficiently small initial velocity and vanishing external force the global existence is proved. The L₂-approach is used. This helps us to treat the transmission conditions. ...

Local free boundary problem for incompressible magnetohydrodynamics

Piotr Kacprzyk

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We consider the motion of an incompressible magnetohydrodynamic (mhd) fluid in a domain bounded by a free surface. In the external domain there exists an electromagnetic field generated by some currents which keeps the mhd flow in the bounded domain. Then on the free surface transmission conditions for electromagnetic fields are imposed. In this paper we prove existence of local regular solutions by the method of successive approximations. The L₂ approach is used. This helps us to treat...

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.

Inviscid limit for free-surface Navier-Stokes equations

Frédéric Rousset (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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The aim of this talk is to present recent results obtained with N. Masmoudi on the free surface Navier-Stokes equations with small viscosity.

Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid

Piotr Kacprzyk (2005)

Banach Center Publications

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Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.

The motion of a fluid in an open channel

Simina Bodea (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider a free boundary value problem for a viscous, incompressible fluid contained in an uncovered three-dimensional rectangular channel, with gravity and surface tension, governed by the Navier-Stokes equations. We obtain existence results for the linear and nonlinear time-dependent problem. We analyse the qualitative behavior of the flow using tools of bifurcation theory. The main result is a Hopf bifurcation theorem with ℤ k -symmetry.

Computation of the drag force on a sphere close to a wall

David Gérard-Varet, Matthieu Hillairet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the effect of surface roughness on solid-solid contact in a Stokes flow. Various models for the roughness are considered, and a unified methodology is given to derive the corresponding asymptotics of the drag force in the close-contact limit. In this way, we recover and clarify the various expressions that can be found in previous studies.