A note on stability shifting for the Muskat problem

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 373, Issue 2050, 2015, Pages

  Córdoba, Diego ^a,b   Gómez Serrano, Javier ^b   Zlato, Andrej ^c  

^a CSIC   (Spain)

^b PRINCETON UNIVERSITY   (United States)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Incompressible fluid; Interface; Muskat problem; Porous media; Rayleigh Taylor

Indexed keywords

INTERFACES (MATERIALS);

INCOMPRESSIBLE FLUID; INITIAL CONDITIONS; MUSKAT PROBLEM; NUMERICAL EVIDENCE; RAYLEIGH-TAYLOR; STABILITY REGIMES;

POROUS MATERIALS;

EID: 84939160525     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2014.0278     Document Type: Article

References (17)

1. Muskat M. 1937 The flow of fluids through porous media. J. Appl. Phys. 8, 274-282. (doi:10.1063/1.1710292)
2. Córdoba D, Gancedo F. 2007 Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Comm. Math. Phys. 273, 445-471. (doi:10.1007/s00220-007-0246-y)
3. Córdoba D, Gancedo F. 2009 A maximum principle for the Muskat problem for fluids with different densities. Comm. Math. Phys. 286, 681-696. (doi:10.1007/s00220-008-0587-1)
4. Castro Á, Córdoba D, Fefferman C, Gancedo F, López-Fernández M. 2012 Rayleigh-taylor breakdown for the Muskat problem with applications to water waves. Ann. Math. 175, 909-948. (doi:10.4007/annals.2012.175.2.9)
5. Castro Á, Córdoba D, Fefferman C, Gancedo F. 2013 Breakdown of smoothness for the Muskat problem. Arch. Ration. Mech. Anal. 208, 805-909. (doi:10.1007/s00205-013-0616-x)
6. Berselli LC, Córdoba D, Granero-Belinchón R. 2014 Local solvability and turning for the inhomogeneous Muskat problem. Interfaces Free Bound. 16, 175-213. (doi:10.4171/IFB/317)
7. Gómez-Serrano J, Granero-Belinchón R. 2014 On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof. Nonlinearity 27, 1471-1498. (doi:10.1088/0951-7715/27/6/1471)
8. Siegel M, Caflisch RE, Howison S. 2004 Global existence, singular solutions, and ill-posedness for the Muskat problem. Comm. Pure Appl. Math. 57, 1374-1411. (doi:10.1002/cpa.20040)
9. Constantin P, Córdoba D, Gancedo F, Strain RM. 2013 On the global existence for the Muskat problem. J. Eur. Math. Soc. 15, 201-227. (doi:10.4171/JEMS/360)
10. Constantin P, Córdoba D, Gancedo F, Rodríguez-Piazza L, Strain RM. 2013 On the Muskat problem: global in time results in 2D and 3D. Preprint. (http://arxiv.org/abs/1310.0953)
11. Escher J, Matioc B-V. 2011 On the parabolicity of the Muskat problem: well-posedness, fingering, and stability results. Zeitschrift für Analysis und ihre Anwendungen 30, 193-218.
12. Friedman A, Tao Y. 2003 Nonlinear stability of the Muskat problem with capillary pressure at the free boundary. Nonlinear Anal. 53, 45-80. (doi:10.1016/S0362-546X(02)00286-9)
13. Granero-Belinchón R. 2014 Global existence for the confined Muskat problem. SIAM J. Math. Anal. 46, 1651-1680. (doi:10.1137/130912529)
14. 2 initial data. Preprint. (http://arxiv.org/abs/1412.7737)
15. Baker G. 1983 Generalized vortex methods for free-surface flows. In Waves on fluid interfaces, pp. 53-81. New York, NY: Academic Press.
16. Sidi A, Israeli M. 1988 Quadrature methods for periodic singular and weakly singular Fredholm integral equations. J. Sci. Comput. 3, 201-231. (doi:10.1007/BF01061258)
17. Castro A, Córdoba D, Fefferman C, Gancedo F, Gómez-Serrano J. 2014 Structural stability for the splash singularities of the water waves problem. Discrete Contin. Dyn. Syst. 34, 4997-5043. (doi:10.3934/dcds.2014.34.4997)