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On the derivation of homogeneous hydrostatic equations

Emmanuel Grenier (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a divergence result for a particular inflexion profile.

On the L 2 -instability and L 2 -controllability of steady flows of an ideal incompressible fluid

Alexander Shnirelman (1999)

Journées équations aux dérivées partielles

In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in L 2 vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady flow is unstable...

On the onset of convection in porous media: temperature depending viscosity

F. Capone (2001)

Bollettino dell'Unione Matematica Italiana

Si considera l'insorgere della convezione naturale in un mezzo poroso (Horton-Rogers-Lapwood problem), assumendo che la viscosità del fluido dipenda dalla temperatura. Adoperando il metodo diretto di Liapunov, si effettua l'analisi della stabilitá non lineare della soluzione di conduzione per i modelli di Darcy e di Forchheimer.

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