Displaying similar documents to “On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations”

Existence of solutions vanishing near some axis for the nonstationary Stokes system with boundary slip conditions

W. M. Zajączkowski

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We examine the nonstationary Stokes system in a bounded domain with the boundary slip conditions. We assume that there exists a line which crosses the domain and that the data belong to Sobolev spaces with weights equal to some powers of the distance to the line. Then the existence of solutions in Sobolev spaces with the corresponding weights is proved.

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.

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.

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.

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.

Asymptotics of parabolic equations with possible blow-up

Radosław Czaja (2004)

Colloquium Mathematicae

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We describe the long-time behaviour of solutions of parabolic equations in the case when some solutions may blow up in a finite or infinite time. This is done by providing a maximal compact invariant set attracting any initial data for which the corresponding solution does not blow up. The abstract result is applied to the Frank-Kamenetskii equation and the N-dimensional Navier-Stokes system with small external force.

On the solvability of some initial boundary value problems of magnetofluidmechanics with Hall and ion-slip effects

Vsevolod A. Solonnikov, Giuseppe Mulone (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The solvability of three linear initial-boundary value problems for the system of equations obtained by linearization of MHD equations is established. The equations contain terms corresponding to Hall and ion-slip currents. The solutions are found in the Sobolev spaces W p 2 , 1 ⁢ Q T with p > 5 / 2 and in anisotropic Holder spaces.

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.