Seminari del Dipartimento di Matematica
Università di Bologna

15 Giu 2015
seminario di analisi matematica
Viscous capillary fluids in fast rotation
Francesco Fanelli (Centro di Ricerca Matematica "Ennio De Giorgi", Scuola Normale Superiore)
In the present talk we are interested in a singular limit problem for a compressible Navier-Stokes-Korteweg system under the action of strong Coriolis force. This is a model for compressible viscous capillary fluids, when the rotation of the Earth is taken into account. Supposing both the Mach and Rossby numbers to be proportional to a small parameter $\veps$, we are interested in the asymptotic behavior of a family of weak solutions to our model, for $\veps$ going to $0$. We consider this problem in the regimes of both constant and vanishing capillarity: we prove the convergence of the model to $2$-D Quasi-Geostrophic type equations for the limit density function. The case of variations of the rotation axis will be discussed as well.