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Systèmes hyperboliques et viscosité évanescente

Frédéric Rousset

Séminaire Bourbaki

Le but de l’exposé est de présenter les résultats obtenus par S. Bianchini et A. Bressan sur le problème de Cauchy pour des perturbations visqueuses ∂ t u ε + ∂ x f ( u ε ) = ε ∂ x x u ε de systèmes strictement hyperboliques ∂ t u + ∂ x f ( u ) = 0 en une dimension d’espace. Ils ont en particulier montré l’existence globale ( t ≥ 0 ), l’unicité et la stabilité des solutions et justifié la convergence quand ε tend vers zéro pour des données initiales à petite variation totale. Leur analyse montre aussi que les solutions du système hyperbolique ainsi obtenues...

Viscous Limits for strong shocks of one-dimensional systems of conservation laws

Frédéric Rousset — 2002

Journées équations aux dérivées partielles

We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of Grenier and Rousset (2001), we replace the smallness condition obtained by energy methods in Goodman and Xin (1992) by a weaker spectral assumption.

Stability of oscillating boundary layers in rotating fluids

Nader Masmoudi;  Frédéric Rousset — 2008

Annales scientifiques de l'École Normale Supérieure

We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to ε . This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.

Quasineutral limit of the Euler-Poisson system for ions in a domain with boundaries II

David Gérard-Varet;  Daniel Han-Kwan;  Frédéric Rousset — 2014

Journal de l’École polytechnique — Mathématiques

In this paper, we study the quasineutral limit of the isothermal Euler-Poisson equation for ions, in a domain with boundary. This is a follow-up to our previous work [], devoted to no-penetration as well as subsonic outflow boundary conditions. We focus here on the case of supersonic outflow velocities. The structure of the boundary layers and the stabilization mechanism are different.

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