Existence of three solutions for a Navier boundary value problem involving the p(x)-biharmonic operator

Honghui Yin; Mei Xu

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

Non-trivial solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions

Shapour Heidarkhani (2012)

Annales Polonici Mathematici

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Using a recent critical point theorem due to Bonanno, the existence of a non-trivial solution for a class of systems of n fourth-order partial differential equations with Navier boundary conditions is established.

On uniqueness of a weak solution to the steady Navier-Stokes problem in a profile cascade with a nonlinear boundary condition on the outflow

Neustupa, Tomáš

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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.

The Navier-Stokes equation with inhomogeneous boundary conditions based on vorticity

Jiří Neustupa, Patrick Penel (2008)

Banach Center Publications

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We formulate a boundary value problem for the Navier-Stokes equations with prescribed u·n, curl u·n and alternatively (∂u/∂n)·n or curl²u·n on the boundary. We deal with the question of existence of a steady weak solution.

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.

On the Navier-Stokes equations with anisotropic wall slip conditions

Christiaan Le Roux (2023)

Applications of Mathematics

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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...

Weak solutions to the Navier-Stokes equations in a Y-shaped domain

Joanna Rencławowicz, Wojciech M. Zajączkowski (2006)

Applicationes Mathematicae

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We prove the existence of weak solutions to the Navier-Stokes equations describing the motion of a fluid in a Y-shaped domain.

Elliptic regularization and Navier-Stokes system.

Adauto Medeiros, Luis, Limaco Ferrel, Juan (1997)

Memoirs on Differential Equations and Mathematical Physics

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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.

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.

Boundary partial regularity for the Navier-Stokes equations.

Seregin, G.A., Shilkin, T.N., Solonnikov, V.N. (2004)

Journal of Mathematical Sciences (New York)

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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.

A remark on the uniqueness problem for the weak solutions of Navier-Stokes equations

Francis Ribaud (2002)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence

R. Farwig, H. Kozono, H. Sohr (2011)

Rendiconti del Seminario Matematico della Università di Padova

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