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Displaying 1801 – 1820 of 3487

On a variant of Korn’s inequality arising in statistical mechanics

L. Desvillettes, Cédric Villani (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We state and prove a Korn-like inequality for a vector field in a bounded open set of $ℝ^{N}$ , satisfying a tangency boundary condition. This inequality, which is crucial in our study of the trend towards equilibrium for dilute gases, holds true if and only if the domain is not axisymmetric. We give quantitative, explicit estimates on how the departure from axisymmetry affects the constants; a Monge–Kantorovich minimization problem naturally arises in this process. Variants in the axisymmetric case are...

On a variant of Korn's inequality arising in statistical mechanics

L. Desvillettes, Cédric Villani (2010)

ESAIM: Control, Optimisation and Calculus of Variations

On a variational method for solving hydrodynamical free boundary problems.

Monakhov, V.N. (2000)

Siberian Mathematical Journal

On an estimate for the linearized compressible Navier-Stokes equations in the $L_{p}$ -framework

Piotr Bogusław Mucha (2001)

Colloquium Mathematicae

An $L_{p}$ -estimate with a constant independent of time for solutions of the linearized compressible Navier-Stokes system in the whole space (under the assumption that solutions have compact supports in space) is obtained.

On an evolutionary nonlinear fluid model in the limiting case

Stephan Luckhaus, Josef Málek (2001)

Mathematica Bohemica

We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with $p$ -structure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case $p = 1$ are covered by this analysis.

On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain

Rieko Shimada, Norikazu Yamaguchi (2008)

Banach Center Publications

This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of $L^{p} - L^{q}$ estimates for the Stokes semigroup associated with a linearized problem, which is also...

On an Extended System of Relativistic Kinematical Quantities Some Applications in Magnetohydrodynamics

Ilija Lukačević (1984)

Zbornik Radova

On an inequality for a free boundary problem for equations of a viscous compressible heat-conducting capillary fluid

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2002)

Applicationes Mathematicae

We derive an inequality for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. This inequality is crucial to proving the global existence of solutions belonging to certain anisotropic Sobolev-Slobodetskiĭ spaces and close to an equilibrium state.

On an integral equation in the problem of the diffraction of a plane wave by a transparent circular cone.

Lyalinov, M.A. (2004)

Journal of Mathematical Sciences (New York)

On anisotropic, dispersive and dissipative wave equations

Campos, L.M.B.C. (1982)

Portugaliae mathematica

On approximate controllability of the Stokes system

Andrei V. Fursikov, Oleg Yu Imanuvilov (1993)

Annales de la Faculté des sciences de Toulouse : Mathématiques

On axially symmetric flows in $ℝ^{3}$ .

Leonardi, S., Málek, J., Nečas, J., Pokorný, M. (1999)

Zeitschrift für Analysis und ihre Anwendungen

On backward-time behavior of the solutions to the 2-D space periodic Navier–Stokes equations

Radu Dascaliuc (2005)

Annales de l'I.H.P. Analyse non linéaire

On Bardina and Approximate Deconvolution Models

Roger Lewandowski (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

We first outline the procedure of averaging the incompressible Navier-Stokes equations when the flow is turbulent for various type of filters. We introduce the turbulence model called Bardina’s model, for which we are able to prove existence and uniqueness of a distributional solution. In order to reconstruct some of the flow frequencies that are underestimated by Bardina’s model, we next introduce the approximate deconvolution model (ADM). We prove existence and uniqueness of a “regular weak solution”...

On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Mirosław Lachowicz (2003)

Banach Center Publications

In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...

On boundary-driven time-dependent Oseen flows

Paul Deuring (2008)

Banach Center Publications

We consider the single layer potential associated to the fundamental solution of the time-dependent Oseen system. It is shown this potential belongs to L²(0,∞,H¹(Ω)³) and to H¹(0,∞,V') if the layer function is in L²(∂Ω×(0,∞)³). (Ω denotes the complement of a bounded Lipschitz set; V denotes the set of smooth solenoidal functions in H¹₀(Ω)³.) This result means that the usual weak solution of the time-dependent Oseen function with zero initial data and zero body force may be represented by a single...

On bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

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

We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can...

On bounded solutions of one-dimensional compressible Navier-Stokes equations

V. Lovicar, I. Straškraba, A. Valli (1990)

Rendiconti del Seminario Matematico della Università di Padova

On bounds of the drag for Stokes flow around a body without thickness

Didier Bresch (1997)

Commentationes Mathematicae Universitatis Carolinae

This paper is devoted to lower and upper bounds of the hydrodynamical drag $T$ for a body in a Stokes flow. We obtain the upper bound since the solution for a flow in an annulus and therefore the hydrodynamical drag can be explicitly derived. The lower bound is obtained by comparison to the Newtonian capacity of a set and with the help of a result due to J. Simon $[10]$ . The chosen approach provides an interesting lower bound which is independent of the interior of the body.

On Composite Mesh Difference Methods for Hyperbolic Differential Equations.

G. Starius (1980)

Numerische Mathematik

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