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Displaying similar documents to “Asymptotic stability theorems for viscous fluid motions in exterior domains”

Stability and instability in nineteenth-century fluid mechanics

Olivier Darrigol (2002)

Revue d'histoire des mathématiques

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The stability or instability of a few basic flows was conjectured, debated, and sometimes proved in the nineteenth century. Motivations varied from turbulence observed in real flows to permanence expected in hydrodynamic theories of matter. Contemporary mathematics often failed to provide rigorous answers, and personal intuitions sometimes gave wrong results. Yet some of the basic ideas and methods of the modern theory of hydrodynamic instability occurred to the elite of British and...

Long-time stability of noncharacteristic viscous boundary layers

Toan Nguyen, Kevin Zumbrun (2009-2010)

Séminaire Équations aux dérivées partielles

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We report our results on long-time stability of multi–dimensional noncharacteristic boundary layers of a class of hyperbolic–parabolic systems including the compressible Navier–Stokes equations with inflow [outflow] boundary conditions, under the assumption of strong spectral, or uniform Evans, stability. Evans stability has been verified for small-amplitude layers by Guès, Métivier, Williams, and Zumbrun. For large–amplitudes, it may be checked numerically, as done in one–dimensional...

Domain sensitivity in singular limits of compressible viscous fluids

Eduard Feireisl (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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In this note, we discuss several recently developed methods for studying stability of a singular limit process with respect to the shape of the underlying physical space. As a model example, we consider a compressible viscous barotropic fluid occupying a spatial domain Ω ⊂ R 3 . In what follows, we describe two rather different problems: (i) the choice of effective boundary conditions; (ii) the fluid flow in the low Mach number regime. In the remaining part of the paper, we analyze these two...