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Volumn 42, Issue 6, 2017, Pages 977-999

Large time decay estimates for the Muskat equation

Author keywords

Asymptotic behavior of solutions; fluid interface; incompressible flows; porous media

Indexed keywords


EID: 85020232624     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605302.2017.1321661     Document Type: Article
Times cited : (46)

References (32)
  • 1
    • 16644399272 scopus 로고    scopus 로고
    • Well-posedness of two-phase hele-shaw flow without surface tension
    • Ambrose, D. M., (2004). Well-posedness of two-phase hele-shaw flow without surface tension. Eur. J. Appl. Math. 15:597–607. doi:https://doi.org/10.1017/S0956792504005662.
    • (2004) Eur. J. Appl. Math. , vol.15 , pp. 597-607
    • Ambrose, D.M.1
  • 2
    • 0032059987 scopus 로고    scopus 로고
    • Local existence of classical solutions to first-order parabolic equations describing free boundaries
    • Bailly, J.-H., (1998). Local existence of classical solutions to first-order parabolic equations describing free boundaries. Nonlinear Anal. 32:583–599. doi:https://doi.org/10.1016/S0362-546X(97)00504-X.
    • (1998) Nonlinear Anal. , vol.32 , pp. 583-599
    • Bailly, J.-H.1
  • 4
    • 84885390314 scopus 로고    scopus 로고
    • Duchon–Robert solutions for the Rayleigh–Taylor and Muskat problems
    • Beck, T., Sosoe, P., Wong, P., (2014). Duchon–Robert solutions for the Rayleigh–Taylor and Muskat problems. J. Differ. Eq. 256:206–222. doi:https://doi.org/10.1016/j.jde.2013.09.001.
    • (2014) J. Differ. Eq. , vol.256 , pp. 206-222
    • Beck, T.1    Sosoe, P.2    Wong, P.3
  • 5
    • 21144469486 scopus 로고
    • Global regularity for vortex patches
    • (MR1207667)
    • Bertozzi, A.L., Constantin, P., (1993). Global regularity for vortex patches. Commun. Math. Phys. 152:19–28 (MR1207667).
    • (1993) Commun. Math. Phys. , vol.152 , pp. 19-28
    • Bertozzi, A.L.1    Constantin, P.2
  • 6
    • 84877066576 scopus 로고    scopus 로고
    • Breakdown of smoothness for the Muskat problem
    • Castro, Á., Córdoba, D., Fefferman, C., Gancedo, F., (2013). Breakdown of smoothness for the Muskat problem. Arch. Ration. Mech. Anal. 208:805–909. doi:https://doi.org/10.1007/s00205-013-0616-x(MR3048596).
    • (2013) Arch. Ration. Mech. Anal. , vol.208 , pp. 805-909
    • Castro, Á.1    Córdoba, D.2    Fefferman, C.3    Gancedo, F.4
  • 7
    • 84857721683 scopus 로고    scopus 로고
    • Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
    • 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. (2) 175:909–948. doi:https://doi.org/10.4007/annals.2012.175.2.9.
    • (2012) Ann. Math. (2) , vol.175 , pp. 909-948
    • Castro, Á.1    Córdoba, D.2    Fefferman, C.3    Gancedo, F.4    López-Fernández, M.5
  • 8
    • 84963877240 scopus 로고    scopus 로고
    • Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations
    • Castro, A., Córdoba, D., Gómez-Serrano, J., (2016). Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations. Duke Math. J. 165:935–984, doi:https://doi.org/10.1215/00127094-3449673(MR3482335).
    • (2016) Duke Math. J. , vol.165 , pp. 935-984
    • Castro, A.1    Córdoba, D.2    Gómez-Serrano, J.3
  • 10
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • Constantin, A., Escher, J., (1998). Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 181:229–243, doi:https://doi.org/10.1007/BF02392586(MR1668586).
    • (1998) Acta Math. , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 13
    • 0003545358 scopus 로고
    • Chicago, IL: University of Chicago Press
    • Constantin, P., Foias, C., (1988). Navier-Stokes Equation. Chicago Lectures in Mathematics, Chicago, IL:University of Chicago Press.
    • (1988) Navier-Stokes Equation
    • Constantin, P.1    Foias, C.2
  • 14
    • 85027054086 scopus 로고    scopus 로고
    • Global regularity for 2D Muskat equations with finite slope. Preprint, ArXiv:1507.01386
    • Constantin, P., Gancedo, F., Shvydkoy, R., Vicol, V., Global regularity for 2D Muskat equations with finite slope. Preprint, ArXiv:1507.01386.
    • Constantin, P.1    Gancedo, F.2    Shvydkoy, R.3    Vicol, V.4
  • 15
    • 0000851461 scopus 로고
    • Global solutions for small data to the Hele-Shaw problem
    • Constantin, P., Pugh, M., (1993). Global solutions for small data to the Hele-Shaw problem. Nonlinearity 6:393–415.
    • (1993) Nonlinearity , vol.6 , pp. 393-415
    • Constantin, P.1    Pugh, M.2
  • 16
    • 78751624212 scopus 로고    scopus 로고
    • Interface evolution: The Hele-Shaw and Muskat problems
    • Córdoba, A., Córdoba, D., Gancedo, F., (2011). Interface evolution:The Hele-Shaw and Muskat problems. Ann. Math. (2) 173:477–542. doi:https://doi.org/10.4007/annals.2011.173.1.10.
    • (2011) Ann. Math. (2) , vol.173 , pp. 477-542
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 17
    • 84882688666 scopus 로고    scopus 로고
    • Porous media: The Muskat problem in three dimensions
    • Córdoba, A., Córdoba, D., Gancedo, F., (2013). Porous media:The Muskat problem in three dimensions. Anal. PDE 6:447–497. doi:https://doi.org/10.2140/apde.2013.6.447(MR3071395).
    • (2013) Anal. PDE , vol.6 , pp. 447-497
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 18
    • 34249881893 scopus 로고    scopus 로고
    • Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
    • Córdoba, D., Gancedo, F., (2007). Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Commun. Math. Phys. 273(2):445–471. doi:https://doi.org/10.1007/s00220-007-0246-y.
    • (2007) Commun. Math. Phys. , vol.273 , Issue.2 , pp. 445-471
    • Córdoba, D.1    Gancedo, F.2
  • 19
    • 58849109361 scopus 로고    scopus 로고
    • A maximum principle for the Muskat problem for fluids with different densities
    • Córdoba, D., Gancedo, F., (2009). A maximum principle for the Muskat problem for fluids with different densities. Commun. Math. Phys. 286:681–696, doi:https://doi.org/10.1007/s00220-008-0587-1(MR2472040).
    • (2009) Commun. Math. Phys. , vol.286 , pp. 681-696
    • Córdoba, D.1    Gancedo, F.2
  • 20
    • 79953645127 scopus 로고    scopus 로고
    • On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
    • Escher, J., Matioc, B.-V., (2011). On the parabolicity of the Muskat problem:Well-posedness, fingering, and stability results. Z. Anal. Anwend. 30:193–218. doi:https://doi.org/10.4171/ZAA/1431(MR2793001).
    • (2011) Z. Anal. Anwend. , vol.30 , pp. 193-218
    • Escher, J.1    Matioc, B.-V.2
  • 21
    • 84892595836 scopus 로고    scopus 로고
    • No-splash theorems for fluid interfaces
    • Fefferman, C.L., (2014). No-splash theorems for fluid interfaces. Proc. Natl. Acad. Sci. USA 111:573–574. doi:https://doi.org/10.1073/pnas.1321805111.
    • (2014) Proc. Natl. Acad. Sci. USA , vol.111 , pp. 573-574
    • Fefferman, C.L.1
  • 22
    • 84958781337 scopus 로고    scopus 로고
    • On the absence of splash singularities in the case of two-fluid interfaces
    • Fefferman, C., Ionescu, A.D., Lie, V., (2016). On the absence of splash singularities in the case of two-fluid interfaces. Duke Math. J. 165:417–462. doi:https://doi.org/10.1215/00127094-3166629.
    • (2016) Duke Math. J. , vol.165 , pp. 417-462
    • Fefferman, C.1    Ionescu, A.D.2    Lie, V.3
  • 23
    • 39749086442 scopus 로고    scopus 로고
    • Existence for the α-patch model and the QG sharp front in Sobolev spaces
    • Gancedo, F., (2008). Existence for the α-patch model and the QG sharp front in Sobolev spaces. Adv. Math. 217:2569–2598. doi:https://doi.org/10.1016/j.aim.2007.10.010.
    • (2008) Adv. Math. , vol.217 , pp. 2569-2598
    • Gancedo, F.1
  • 24
    • 84892577446 scopus 로고    scopus 로고
    • Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
    • Gancedo, F., Strain, R.M., (2014). Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem. Proc. Natl. Acad. Sci. USA 111:635–639. doi:https://doi.org/10.1073/pnas.1320554111.
    • (2014) Proc. Natl. Acad. Sci. USA , vol.111 , pp. 635-639
    • Gancedo, F.1    Strain, R.M.2
  • 25
    • 84902663105 scopus 로고    scopus 로고
    • Global existence for the confined Muskat problem
    • Granero-Belinchón, R., (2014). Global existence for the confined Muskat problem. SIAM J. Math. Anal. 46:1651–1680.
    • (2014) SIAM J. Math. Anal. , vol.46 , pp. 1651-1680
    • Granero-Belinchón, R.1
  • 26
    • 33749026600 scopus 로고
    • The flow of water
    • Hele-Shaw, H.S., (1898). The flow of water. Nature 58:34–36.
    • (1898) Nature , vol.58 , pp. 34-36
    • Hele-Shaw, H.S.1
  • 27
    • 0008283862 scopus 로고
    • Removing the stiffness from interfacial flows with surface tension
    • Hou, T.Y., Lowengrub, J.S., Shelley, M.J., (1994). Removing the stiffness from interfacial flows with surface tension. J. Comput. Phys. 114:312–338. doi:https://doi.org/10.1006/jcph.1994.1170.
    • (1994) J. Comput. Phys. , vol.114 , pp. 312-338
    • Hou, T.Y.1    Lowengrub, J.S.2    Shelley, M.J.3
  • 29
    • 0001383598 scopus 로고
    • The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
    • (2 plates)
    • Saffman, P.G., Taylor, G., (1958). The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. London. Ser. A 245:312–329 (2 plates).
    • (1958) Proc. R. Soc. London. Ser. A , vol.245 , pp. 312-329
    • Saffman, P.G.1    Taylor, G.2
  • 30
    • 4544228729 scopus 로고    scopus 로고
    • Global existence, singular solutions, and ill-posedness for the Muskat problem
    • Siegel, M., Caflisch, R.E., Howison, S., (2004). Global existence, singular solutions, and ill-posedness for the Muskat problem. Commun. Pure Appl. Math. 57:1374–1411, doi:https://doi.org/10.1002/cpa.20040.
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 1374-1411
    • Siegel, M.1    Caflisch, R.E.2    Howison, S.3
  • 31
    • 84901297547 scopus 로고    scopus 로고
    • The Boltzmann equation, Besov spaces, and optimal time decay rates in
    • Sohinger, V., Strain, R.M., (2014). The Boltzmann equation, Besov spaces, and optimal time decay rates in. Adv. Math. 261:274–332. doi:https://doi.org/10.1016/j.aim.2014.04.012.
    • (2014) Adv. Math. , vol.261 , pp. 274-332
    • Sohinger, V.1    Strain, R.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.