A note on interface dynamics for convection in porous media

Physica D: Nonlinear Phenomena

Volumn 237, Issue 10-12, 2008, Pages 1488-1497

  Córdoba, Diego ^a   Gancedo, Francisco ^b   Orive, Rafael ^c  

^a INSTITUTO DE CIENCIAS MATEMÁTICAS   (Spain)

^b UNIVERSITY OF CHICAGO   (United States)

^c UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Fluid interface; Incompressible flow; Porous media

Indexed keywords

INCOMPRESSIBLE FLOW; INTEGRAL EQUATIONS; INTERFACES (MATERIALS); PARAMETERIZATION;

FLUID INTERFACE; FREE BOUNDARY; INTEGRAL OPERATOR; PERIODIC INTERFACE;

POROUS MATERIALS;

EID: 44649179813     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.03.042     Document Type: Article

References (17)

1. Ambrose D. Well-posedness of two-phase hele-shaw flow without surface tension. European J. Appl. Math. 15 (2004) 597-607
2. Bear J. Dynamics of Fluids in Porous Media (1972), American Elsevier, New York
3. Constantin P., and Pugh M. Global solutions for small data to the Hele-Shaw problem. Nonlinearity 6 (1993) 393-415
4. Córdoba A., and Córdoba D. A pointwise estimate for fractionary derivatives with applications to partial differential equations. Proc. Natl. Acad. Sci. USA 100 26 (2003) 15316-15317
5. Córdoba A., and Córdoba D. A maximum principle applied to Quasi-geostrophic equations. Comm. Math. Phys. 249 3 (2004) 511-528
6. Córdoba D., and Gancedo F. Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Comm. Math. Phys 273 2 (2007) 445-471
7. D. Córdoba, F. Gancedo, A maximum principle for the Muskat problem for fluids with different densities, Comm. Math. Phys. (in press)
8. Córdoba D., Gancedo F., and Orive R. Analytical behaviour of 2D incompressible flow in porous media. J. Math. Phys. 48 6 (2007)
9. Dritschel D.G. Comput. Phys. Rep. 10 (1989) 77-146
10. Dombre T., Pumir A., and Siggia E. On the interface dynamics for convection in porous media. Physica D 57 (1992) 311-329
11. Escher J., and Simonett G. Classical solutions for Hele-Shaw models with surface tension. Adv. Differential Equations 2 (1997) 619-642
12. Hele-Shaw. The flow of water. Nature 58 1489 (1898) 34-36 520
13. Hou T.Y., Lowengrub J.S., and Shelley M.J. Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 114 (1994) 312-338
14. M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, New York, 1937
15. Saffman P.G., and Taylor. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. Ser. A 245 (1958) 312-329
16. Siegel M., Caflisch R., and Howison S. Global existence, singular solutions, and Ill-posedness for the muskat problem. Comm. Pure Appl. Math. 57 (2004) 1374-1411
17. Stein E. Singular Integrals and Differentiability Properties of Function (1970), Princeton University Press, Princeton, NJ