Stabilization for 1D radiative and reactive viscous gas flows

Bernard Ducomet; Alexander Zlotnik

doi:10.1016/j.crma.2003.11.013

Partial Differential Equations

Stabilization for 1D radiative and reactive viscous gas flows

Presented by: Gérard Iooss

Bernard Ducomet ¹; Alexander Zlotnik ²

¹ CEA-département de physique théorique et appliquée, BP 12, 91680 Bruyères le Châtel, France
² Moscow Power Engineering Institute, Krasnokazarmennaja 14, 111250 Moscow, Russia

Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 127-132.

Abstract
Résumé

We consider the compressible 1D-Navier–Stokes system for a viscous heat-conducting gas, with a pressure law $p (ρ, θ) = R ρ θ + \frac{a}{3} θ^{4}$ and a one-order kinetics to include radiative and reactive processes. The mass force and the ignition phenomenon are also taken into account. For large data and under general assumptions on the heat conductivity, we establish global in time bounds and exponential stabilization for solutions in L^q and H¹-norms, by using new Lyapunov functionals.

Nous étudions le système de Navier–Stokes 1D décrivant un fluide compressible conducteur avec contribution radiative, couplé à une cinétique chimique du premier ordre. On tient compte d'un champ de force externe ainsi que d'une température d'ignition. Pour de grandes données et sous des conditions générales sur la conductivité, nous prouvons l'existence globale d'une solution et sa stabilisation en normes L^q et H¹, en introduisant de nouvelles fonctionnelles de Lyapunov.

Received: 2003-06-30
Accepted: 2003-11-18
Published online: 2003-12-30

DOI: 10.1016/j.crma.2003.11.013

Author's affiliations:

Bernard Ducomet ¹; Alexander Zlotnik ²

¹ CEA-département de physique théorique et appliquée, BP 12, 91680 Bruyères le Châtel, France
² Moscow Power Engineering Institute, Krasnokazarmennaja 14, 111250 Moscow, Russia

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     author = {Bernard Ducomet and Alexander Zlotnik},
     title = {Stabilization for {1D} radiative and reactive viscous gas flows},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {127--132},
     publisher = {Elsevier},
     volume = {338},
     number = {2},
     year = {2004},
     doi = {10.1016/j.crma.2003.11.013},
     language = {en},
}

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Bernard Ducomet; Alexander Zlotnik. Stabilization for 1D radiative and reactive viscous gas flows. Comptes Rendus. Mathématique, Volume 338 (2004) no. 2, pp. 127-132. doi : 10.1016/j.crma.2003.11.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.013/

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