This issuePrevious ArticleSingularity formation in the generalized Benjamin-Ono equationNext ArticleJustification of and long-wave correction to Davey-Stewartson systems from quadratic hyperbolic systems
We study various singularly perturbed models
related to rotating flows in a cylinder.
At first we consider the three dimensional incompressible
Navier--Stokes equations with turbulent viscosity, in the low Rossby
We prove a strong convergence result for ill prepared data,
under a geometrical
assumption on the cylinder section and a genericity condition on the
In a second section, we discuss the compressible Navier--Stokes
equations with anisotropic viscosity tensor in the combined low Mach
and low Rossby number limit.
In the case of well prepared initial data, we prove that
global weak solutions with Dirichlet boundary conditions converge to the
solution of a two--dimensional quasi-geostrophic model taking into
account the compressibility.
In the case of ill prepared data, we only show that we can hope a
strong convergence result under the same kind of assumptions as in the