Stability of oscillating boundary layers in rotating fluids

Masmoudi, Nader; Rousset, Frédéric

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 6, pp. 955-1002.

On prouve la stabilité linéaire et non-linéaire de couches limites oscillantes de type Ekman pour les fluides tournant dans le cas de données mal préparées sous une hypothèse spectrale. On s’intéresse au cas où la viscosité et le nombre de Rossby sont du même ordre $\epsilon$. Cette étude généralise celle de [23] où une condition de petitesse était imposée et celle de [26] où les données bien préparées étaient traitées.

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 $\epsilon$. 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.

Classification : 35B25, 35B35, 35Q30
Keywords: incompressible Navier-Stokes equation, oscillatory perturbations, vanishing viscosity
Mot clés : Équation de Navier-Stokes incompressible, perturbations oscillantes, viscosité évanescente

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