A Note on Viscous Capillary Fluids in Fast Rotation

Francesco Fanelli

Abstract


The present note is devoted to the study of singular perturbation problems for a Navier-Stokes-Korteweg system with Coriolis force. Such a model describes the motion of viscous compressible capillary fluids under the action of the Earth rotation. We are interested in the asymptotic behavior of a family of weak solutions in the limit for the Mach, the Rossby and the Weber numbers going to 0.

Keywords


Navier-Stokes-Korteweg system; rotating fluids; capillarity effects; singular perturbation problem; low Mach, Rossby and Weber numbers

Full Text:

PDF (English)

References


D. Bresch, B. Desjardins. Existence of global weak solution for a 2D viscous shallow water equation and convergence to the quasi-geostrophic model. Comm. Math. Phys., 238 (2003), n. 1-2, 211-223.

D. Bresch, B. Desjardins. Quelques modèles diffusifs capillaires de type Korteweg. C. R. Acad. Sci. Paris, Sect. Mécanique, 332 (2004), n. 11, 881-886.

D. Bresch, B. Desjardins, C.-K. Lin. On some compressible fluid models: Korteweg, lubrication, and shallow water systems. Comm. Partial Differential Equations, 28 (2003), n. 3-4, 843-868.

D. Bresch, B. Desjardins, E. Zatorska. Two-velocity hydrodynamics in fluid mechanics: Part II. Existence of global κ-entropy solutions to compressible Navier-Stokes systems with degenerate viscosities. J. Math. Pures Appl., accepted for publication (2015).

H. L. Cycon, R. G. Froese, W. Kirsch, B. Simon. Schrödinger operators with application to quantum mechanics and global geometry. Text and Monographs in Physics, Springer-Verlag, Berlin (1987).

F. Fanelli. Highly rotating viscous compressible fluids in presence of capillarity effects. Submitted (2015), http://arxiv.org/abs/1410.8777.

F. Fanelli. A singular limit problem for rotating capillary fluids with variable rotation axis. Submitted (2015), http://arxiv.org/abs/1504.02903.

E. Feireisl, I. Gallagher, D. Gérard-Varet, A. Novotný. Multi-scale analysis of compressible viscous and rotating fluids. Comm. Math. Phys., 314 (2012), n. 3, 641-670.

E. Feireisl, I. Gallagher, A. Novotný. A singular limit for compressible rotating fluids. SIAM J. Math. Anal., 44 (2012), n. 1, 192-205.

I. Gallagher, L. Saint-Raymond. Weak convergence results for inhomogeneous rotating fluid equations. J. Anal. Math., 99 (2006), 1-34.

A. Jüngel, C.-K. Lin, K.-C. Wu. An asymptotic limit of a Navier-Stokes system with capillary effects. Comm. Math. Phys., 329 (2014), n. 2, 725-744.




DOI: 10.6092/issn.2240-2829/5892

Refbacks

  • There are currently no refbacks.


Copyright (c) 2015 Francesco Fanelli

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Creative Commons License 

ISSN 2240-2829
Registration at Bologna Law Court no. 8138 on 24th November, 2010

The journal is hosted and mantained by ABIS-AlmaDL [privacy]