Structure of entropies in dissipative multicomponent fluids

Vincent Giovangigli; Lionel Matuszewski

doi:10.3934/krm.2013.6.373

Article Contents

2013, Volume 6, Issue 2: 373-406. Doi: 10.3934/krm.2013.6.373

This issue Previous Article Spectral decompositions and $\mathbb{L}^2$-operator norms of toy hypocoercive semi-groups Next Article Analytical regularizing effect for the radial and spatially homogeneous Boltzmann equation

Structure of entropies in dissipative multicomponent fluids

Vincent Giovangigli^1, and
Lionel Matuszewski^2,

1.
CMAP, CNRS, Ecole Polytechnique, 91128 Palaiseau cedex
2.
ONERA, Centre de Palaiseau, 91198 Palaiseau cedex

Received: May 31, 2012

Revised: November 30, 2012

Published: May 2013

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Abstract

We investigate the structure of mathematical entropies for dissipative multicomponent fluid models derived from the kinetic theory of gases. The corresponding governing equations notably involve nonideal thermochemistry as well as diffusion fluxes driven by chemical potential gradients and temperature gradients. We obtain the general form of mathematical entropies compatible with the hyperbolic structure of the system of partial differential equations assuming a natural nondegeneracy condition. We next establish that entropies compatible with the hyperbolic-parabolic structure are unique up to an affine transform when they are independent on mass and heat diffusion parameters.

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Mathematics Subject Classification: Primary: 35L65, 76T30, 35M30; Secondary: 80A32.

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