Geophysical flows and the effects of a strong surface tension

Francesco Fanelli (1, 2, 3)

1 ICJ - Institut Camille Jordan
2 EDPA - Équations aux dérivées partielles, analyse
3 UCBL - Université Claude Bernard Lyon 1

In the present note we review some recent results for a class of singular perturbation problems for a Navier-Stokes-Korteweg system with Coriolis force. More precisely, we study the asymptotic behaviour of solutions when taking incompressible and fast rotation limits simultaneously, in a constant capillarity regime. Our main purpose here is to explain in detail the description of the phenomena we want to capture, and the mathematical derivation of the system of equations. Hence, a huge part of this work is devoted to physical considerations and mathematical modeling.

Mots clés: Capillarity; Earth rotation; Navier-Stokes-Korteweg system; singular perturbation problem; low Mach; Rossby and Weber numbers; variable rotation axis; Zygmund regularity

Domaines: Equations aux dérivées partielles [math.AP]; Océan, Atmosphère; Supraconductivité [cond-mat.supr-con]; Gaz Quantiques [cond-mat.quant-gas]; Dynamique des Fluides [physics.flu-dyn]; Géophysique [physics.geo-ph]

Francesco Fanelli. Geophysical flows and the effects of a strong surface tension. 2016. ⟨hal-01323692⟩