Displaying similar documents to “Reaction-Diffusion Equations for Chemically Reacting Gas Mixtures”

Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases

Marzia Bisi, Laurent Desvillettes (2014)

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

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We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in...

An existence proof for the stationary compressible Stokes problem

A. Fettah, T. Gallouët, H. Lakehal (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.

Modelling of Miscible Liquids with the Korteweg Stress

Ilya Kostin, Martine Marion, Rozenn Texier-Picard, Vitaly A. Volpert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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When two miscible fluids, such as glycerol (glycerin) and water, are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients exist during some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical model consisting of the diffusion equation with convective terms and of the Navier-Stokes equations with the Korteweg stress. We prove...

On the existence and regularity of the solutions to the incompressible Navier-Stokes equations in presence of mass diffusion

Rodolfo Salvi (2008)

Banach Center Publications

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This paper is devoted to the study of the incompressible Navier-Stokes equations with mass diffusion in a bounded domain in R³ with C³ boundary. We prove the existence of weak solutions, in the large, and the behavior of the solutions as the diffusion parameter λ → 0. Moreover, the existence of L²-strong solution, in the small, and in the large for small data, is proved. Asymptotic regularity (the regularity after a finite period) of a weak solution is studied. Finally, using the Dore-Venni...

On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation

M. Pulvirenti (2008)

Bollettino dell'Unione Matematica Italiana

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This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.