Multi-scale analysis of compressible viscous and rotating fluids

Eduard Feireisl (1) , Isabelle Gallagher (2) , David Gérard-Varet (2) , Antonin Novotny (3)

1 Mathematical Institute [Praha] - Academy of Sciences
2 IMJ - Institut de Mathématiques de Jussieu
3 IMATH - Institut de Mathématiques de Toulon - EA 2134

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter $\ep$. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account.

Domaines: Equations aux dérivées partielles [math.AP]

Eduard Feireisl, Isabelle Gallagher, David Gérard-Varet, Antonin Novotny. Multi-scale analysis of compressible viscous and rotating fluids. SIAM Journal on Mathematical Analysis, 2012. ⟨hal-00586234⟩