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Volumn 16, Issue 2, 2014, Pages 175-213

Local solvability and turning for the inhomogeneous Muskat problem

Author keywords

Blow up; Darcy's law; Inhomogeneous muskat problem; Maximum principle; Well posedness

Indexed keywords


EID: 84904552069     PISSN: 14639963     EISSN: None     Source Type: Journal    
DOI: 10.4171/IFB/317     Document Type: Article
Times cited : (40)

References (27)
  • 1
    • 16644399272 scopus 로고    scopus 로고
    • Well-posedness of two-phase Hele-Shaw flow without surface tension
    • DOI 10.1017/S0956792504005662
    • Ambrose, D., Well-posedness of two-phase Hele-Shaw flow without surface tension. European J. Appl. Math. 15(2004), 597-607. Zbl1076.76027 MR2128613 (Pubitemid 40482778)
    • (2004) European Journal of Applied Mathematics , vol.15 , Issue.5 , pp. 597-607
    • Ambrose, D.M.1
  • 2
    • 34248230656 scopus 로고    scopus 로고
    • Hardy spaces for the strip
    • Zbl1160.30021 MR2323495
    • Bakan, A. & Kaijser, S., Hardy spaces for the strip. J. Math. Anal. Appl. 333(2007), 347-364. Zbl1160.30021 MR2323495
    • (2007) J. Math. Anal. Appl. , vol.333 , pp. 347-364
    • Bakan, A.1    Kaijser, S.2
  • 4
    • 84877066576 scopus 로고    scopus 로고
    • Breakdown of smoothness for the Muskat problem
    • Zbl06254072 MR3048596
    • Castro, A., Cordoba, D., Fefferman, C. & Gancedo, F., Breakdown of smoothness for the Muskat problem. Arch. Ration. Mech. Anal. 208(2013), 805-909. Zbl06254072 MR3048596
    • (2013) Arch. Ration. Mech. Anal. , vol.208 , pp. 805-909
    • Castro, A.1    Cordoba, D.2    Fefferman, C.3    Gancedo, F.4
  • 5
    • 84857721683 scopus 로고    scopus 로고
    • Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
    • Zbl1267.76033 MR2993754
    • Castro, A., Cordoba, D., Fefferman, C., Gancedo, F. & Lopez-Fernandez, M., Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves. Ann. of Math (2), 175(2012), 909-948. Zbl1267.76033 MR2993754
    • (2012) Ann. of Math , vol.175 , Issue.2 , pp. 909-948
    • Castro, A.1    Cordoba, D.2    Fefferman, C.3    Gancedo, F.4    Lopez-Fernandez, M.5
  • 6
    • 84861014036 scopus 로고    scopus 로고
    • Modeling the dynamics of a geothermal reservoir fed by gravity driven flow through overstanding saturated rocks
    • Cerminara, M. & Fasano, A., Modeling the dynamics of a geothermal reservoir fed by gravity driven flow through overstanding saturated rocks. J. Volcanology Geothermal Res. 233-234(2012), 37-54.
    • (2012) J. Volcanology Geothermal Res. , vol.233-234 , pp. 37-54
    • Cerminara, M.1    Fasano, A.2
  • 8
    • 84870705750 scopus 로고    scopus 로고
    • On the global existence for the Muskat problem
    • Zbl1258.35002 MR2998834
    • Constantin, P., Cordoba, D., Gancedo, F. & Strain, R., On the global existence for the Muskat problem. J. Eur. Math. Soc. 15(2013), 201-227. Zbl1258.35002 MR2998834
    • (2013) J. Eur. Math. Soc. , vol.15 , pp. 201-227
    • Constantin, P.1    Cordoba, D.2    Gancedo, F.3    Strain, R.4
  • 9
    • 0000851461 scopus 로고
    • Global solutions for small data to the Hele-Shaw problem
    • Constantin, P. & M. Pugh. M., Global solutions for small data to the Hele-Shaw problem. Nonlinearity 6 393-415, 1993.
    • (1993) Nonlinearity , vol.6 , pp. 393-415
    • Constantin, P.1    Pugh, M.M.2
  • 10
    • 78751624212 scopus 로고    scopus 로고
    • Interface evolution: The Hele-Shaw and Muskat problems
    • Zbl1229.35204 MR2753607
    • Cordoba, A., CÓrdoba, D. & Gancedo, F., Interface evolution: the Hele-Shaw and Muskat problems. Ann. of Math (2) 173(2011), 477-542. Zbl1229.35204 MR2753607
    • (2011) Ann. of Math , vol.173 , Issue.2 , pp. 477-542
    • Cordoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 11
    • 34249881893 scopus 로고    scopus 로고
    • Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
    • Zbl1120.76064 MR2318314
    • CÓrdoba, D. & Gancedo, F., Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Comm. Math. Phys. 273(2007), 445-471. Zbl1120.76064 MR2318314
    • (2007) Comm. Math. Phys. , vol.273 , pp. 445-471
    • Córdoba, D.1    Gancedo, F.2
  • 12
    • 58849109361 scopus 로고    scopus 로고
    • A maximum principle for the Muskat problem for fluids with different densities
    • Zbl1173.35637 MR2472040
    • CÓ rdoba, D. & F. Gancedo, F., A maximum principle for the Muskat problem for fluids with different densities. Comm. Math. Phys. 286(2009), 681-696. Zbl1173.35637 MR2472040
    • (2009) Comm. Math. Phys. , vol.286 , pp. 681-696
    • Rdoba, C.D.1    Gancedo, F.F.2
  • 13
    • 44649179813 scopus 로고    scopus 로고
    • A note on interface dynamics for convection in porous media
    • Zbl1143.76574
    • Córdoba, D., Gancedo, F. & Orive, R., A note on interface dynamics for convection in porous media. Physica D: Nonlinear Phenomena 237(2008), 1488-1497. Zbl1143.76574
    • (2008) Physica D: Nonlinear Phenomena , vol.237 , pp. 1488-1497
    • Córdoba, D.1    Gancedo, F.2    Orive, R.3
  • 14
    • 84891391945 scopus 로고    scopus 로고
    • The confined Muskat problem: Differences with the deep water regime
    • MR3144991
    • CÓrdoba, D. Granero-BelinchÓn, R. & Orive, R., The confined Muskat problem: Differences with the deep water regime. Comm. Math. Sci. 12(2014), 423-455. MR3144991
    • (2014) Comm. Math. Sci. , vol.12 , pp. 423-455
    • Córdoba, D.1    Granero-BelinchÓn, R.2    Orive, R.3
  • 15
    • 79953645127 scopus 로고    scopus 로고
    • On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
    • Escher, J. & Matioc, B., On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results. Z. Anal. Anwend. 30(2011), 193-218.
    • (2011) Z. Anal. Anwend. , vol.30 , pp. 193-218
    • Escher, J.1    Matioc, B.2
  • 16
    • 84858405608 scopus 로고    scopus 로고
    • A generalized Rayleigh-Taylor condition for the Muskat problem
    • Zbl1243.35179 MR2864377
    • Escher, J., Matioc, A. V. & Matioc, B., A generalized Rayleigh-Taylor condition for the Muskat problem. Nonlinearity 25(2011), 73-92. Zbl1243.35179 MR2864377
    • (2011) Nonlinearity , vol.25 , pp. 73-92
    • Escher, J.1    Matioc, A.V.2    Matioc, B.3
  • 17
    • 0000010015 scopus 로고    scopus 로고
    • Classical solutions for Hele-Shaw models with surface tension
    • Zbl1023.35527 MR1441859
    • Escher, J. & Simonett, G., Classical solutions for Hele-Shaw models with surface tension. Adv. Differential Equations 2(1997), 619-642. Zbl1023.35527 MR1441859
    • (1997) Adv. Differential Equations , vol.2 , pp. 619-642
    • Escher, J.1    Simonett, G.2
  • 19
    • 84904538681 scopus 로고
    • Flow of water by colourbands
    • JFM 29.0646.02
    • Hele-Shaw, H., Flow of water by colourbands. Nature 58(1897), 520-520,. JFM 29.0646.02
    • (1897) Nature , vol.58 , pp. 520-520
    • Hele-Shaw, H.1
  • 20
    • 0004546593 scopus 로고
    • Unsteady flow in porous media with a free surface
    • Zbl0713.76100 MR1093829
    • Kawarada, H. & Koshigoe, H., Unsteady flow in porous media with a free surface. Japan J. Indust. Appl. Math. 8(1991), 41-84. Zbl0713.76100 MR1093829
    • (1991) Japan J. Indust. Appl. Math. , vol.8 , pp. 41-84
    • Kawarada, H.1    Koshigoe, H.2
  • 21
    • 79957771718 scopus 로고    scopus 로고
    • Darcy flow on a plate with prescribed contact angle-wellposedness and lubrication approximation
    • arXiv:1204.2278 math. AP
    • Knüpfer, H. & N. Masmoudi, N., Darcy flow on a plate with prescribed contact angle-wellposedness and lubrication approximation. Preprint, arXiv:1204.2278 [math. AP].
    • Preprint
    • Knüpfer, H.1    Masmoudi, N.N.2
  • 25
    • 84972536320 scopus 로고
    • An abstract form of the nonlinear Cauchy-Kowalewski theorem
    • Zbl0257.35001 MR0322321
    • Nirenberg, L., An abstract form of the nonlinear Cauchy-Kowalewski theorem. J. Differential Geom 6(1972), 561-576. Zbl0257.35001 MR0322321
    • (1972) J. Differential Geom , vol.6 , pp. 561-576
    • Nirenberg, L.1
  • 26
    • 84972513394 scopus 로고
    • A note on a theorem of Nirenberg
    • Zbl0368. 35007 MR0512931
    • Nishida, T., A note on a theorem of Nirenberg. J. Differential Geom 12(1977), 629-633. Zbl0368. 35007 MR0512931
    • (1977) J. Differential Geom , vol.12 , pp. 629-633
    • Nishida, T.1
  • 27
    • 4544228729 scopus 로고    scopus 로고
    • Global existence, singular solutions, and ill-posedness for the Muskat problem
    • DOI 10.1002/cpa.20040
    • Siegel, M., Caflisch, R. & Howison, S., Global existence, singular solutions, and ill-posedness for the Muskat problem. Comm. Pure Appl. Math. 57(2004), 1374-1411. Zbl1062.35089 MR2070208 (Pubitemid 39234321)
    • (2004) Communications on Pure and Applied Mathematics , vol.57 , Issue.10 , pp. 1374-1411
    • Siegel, M.1    Caflisch, R.E.2    Howison, S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.