-
1
-
-
84980080664
-
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II
-
MR0162050
-
S. AGMON, A. DOUGLIS, and L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II, Comm. Pure Appl. Math. 17 (1964), 35–92. http://dx.doi.org/10.1002/cpa.3160170104. MR0162050
-
(1964)
Comm. Pure Appl. Math.
, vol.17
, pp. 35-92
-
-
Agmon, S.1
Douglis, A.2
Nirenberg, L.3
-
2
-
-
0004081844
-
-
Birkhäuser Boston, Inc., Boston, MA MR1345385
-
H. AMANN, Linear and Quasilinear Parabolic Problems. Vol. I: Abstract Linear Theory, Monographs in Mathematics, vol. 89, Birkhäuser Boston, Inc., Boston, MA, 1995. http://dx.doi.org/10.1007/978-3-0348-9221-6. MR1345385
-
(1995)
Linear and Quasilinear Parabolic Problems. Vol. I: Abstract Linear Theory, Monographs in Mathematics
, vol.89
-
-
Amann, H.1
-
3
-
-
16644399272
-
Well-posedness of two-phase Hele-Shaw flow without surface tension
-
MR2128613
-
D. M. AMBROSE, Well-posedness of two-phase Hele-Shaw flow without surface tension, European J. Appl. Math. 15 (2004), no. 5, 597–607. http://dx.doi.org/10.1017/S0956792504005662. MR2128613
-
(2004)
European J. Appl. Math.
, vol.15
, Issue.5
, pp. 597-607
-
-
Ambrose, D.M.1
-
4
-
-
2442662590
-
Operator-valued Fourier multipliers on periodic Besov spaces and applications
-
MR2064734
-
W. ARENDT and S. BU, Operator-valued Fourier multipliers on periodic Besov spaces and applications, Proc. Edinb. Math. Soc. (2) 47 (2004), no. 1, 15–33. http://dx.doi.org/10.1017/S0013091502000378. MR2064734
-
(2004)
Proc. Edinb. Math. Soc. (2)
, vol.47
, Issue.1
, pp. 15-33
-
-
Arendt, W.1
Bu, S.2
-
5
-
-
84892764232
-
the two-phase Hele-Shaw problem with a nonregular initial interface and without surface tension
-
152, 155 English, with English, Russian and Ukrainian summaries MR3236960
-
B. V. BAZALIY and N. VASYLYEVA, The two-phase Hele-Shaw problem with a nonregular initial interface and without surface tension, Zh. Mat. Fiz. Anal. Geom. 10 (2014), no. 1, 3–43, 152, 155 (English, with English, Russian and Ukrainian summaries). http://dx.doi.org/10.15407/mag10.01.003. MR3236960
-
(2014)
Zh. Mat. Fiz. Anal. Geom.
, vol.10
, Issue.1
, pp. 3-43
-
-
Bazaliy, B.V.1
Vasylyeva, N.2
-
6
-
-
84904552069
-
Local solvability and turning for the inhomogeneous Muskat problem
-
MR3231970
-
L. C. BERSELLI, D. CÓRDOBA, and R. GRANERO-BELINCHÓN, Local solvability and turning for the inhomogeneous Muskat problem, Interfaces Free Bound. 16 (2014), no. 2, 175–213. http://dx.doi.org/10.4171/IFB/317. MR3231970
-
(2014)
Interfaces Free Bound
, vol.16
, Issue.2
, pp. 175-213
-
-
Berselli, L.C.1
Córdoba, D.2
Granero-Belinchón, R.3
-
7
-
-
79953190074
-
Turning waves and breakdown for incompressible flows
-
MR2792311
-
Á. CASTRO, D. CÓRDOBA, Ch. L. FEFFERMAN, F. GANCEDO, and M. LÓPEZ-FERNÁNDEZ, Turning waves and breakdown for incompressible flows, Proc. Natl. Acad. Sci. USA 108 (2011), no. 12, 4754–4759. http://dx.doi.org/10.1073/pnas.1101518108. MR2792311
-
(2011)
Proc. Natl. Acad. Sci. USA
, vol.108
, Issue.12
, pp. 4754-4759
-
-
Castro, Á.1
Córdoba, D.2
Fefferman, Ch.L.3
Gancedo, F.4
López-Fernández, M.5
-
8
-
-
84857721683
-
Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves
-
MR2993754
-
- Rayleigh-Taylor breakdown for the Muskat problem with applications to water waves, Ann. of Math. (2) 175 (2012), no. 2, 909–948. http://dx.doi.org/10.4007/annals.2012.175.2.9. MR2993754
-
(2012)
Ann. of Math. (2)
, vol.175
, Issue.2
, pp. 909-948
-
-
Castro, Á.1
Córdoba, D.2
Fefferman, Ch.L.3
Gancedo, F.4
López-Fernández, M.5
-
9
-
-
84877066576
-
Breakdown of smoothness for the Muskat problem
-
MR3048596
-
Á. CASTRO, D. CÓRDOBA, Ch. L. FEFFERMAN, and F. GANCEDO, Breakdown of smoothness for the Muskat problem, Arch. Ration. Mech. Anal. 208 (2013), no. 3, 805–909. http://dx.doi.org/10.1007/s00205-013-0616-x. MR3048596
-
(2013)
Arch. Ration. Mech. Anal.
, vol.208
, Issue.3
, pp. 805-909
-
-
Castro, Á.1
Córdoba, D.2
Fefferman, Ch.L.3
Gancedo, F.4
-
10
-
-
84870705750
-
on the global existence for the Muskat problem
-
MR2998834
-
P. CONSTANTIN, D. CÓRDOBA, F. GANCEDO, and R. M. STRAIN, On the global existence for the Muskat problem, J. Eur. Math. Soc. (JEMS) 15 (2013), no. 1, 201–227. http://dx.doi.org/10.4171/JEMS/360. MR2998834
-
(2013)
J. Eur. Math. Soc. (JEMS)
, vol.15
, Issue.1
, pp. 201-227
-
-
Constantin, P.1
Córdoba, D.2
Gancedo, F.3
Strain, R.M.4
-
11
-
-
78751624212
-
Interface evolution: the Hele-Shaw and Muskat problems
-
MR2753607
-
A. CÓRDOBA, D. CÓRDOBA, and F. GANCEDO, Interface evolution: The Hele-Shaw and Muskat problems, Ann. of Math. (2) 173 (2011), no. 1, 477–542. http://dx.doi.org/10.4007/annals.2011.173.1.10. MR2753607
-
(2011)
Ann. of Math. (2)
, vol.173
, Issue.1
, pp. 477-542
-
-
Córdoba, A.1
Córdoba, D.2
Gancedo, F.3
-
12
-
-
34249881893
-
Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
-
MR2318314
-
D. CÓRDOBA and F. GANCEDO, Contour dynamics of incompressible 3-D fluids in a porous medium with different densities, Comm. Math. Phys. 273 (2007), no. 2, 445–471. http://dx.doi.org/10.1007/s00220-007-0246-y. MR2318314
-
(2007)
Comm. Math. Phys.
, vol.273
, Issue.2
, pp. 445-471
-
-
Córdoba, D.1
Gancedo, F.2
-
13
-
-
77955845839
-
Absence of squirt singularities for the multi-phase Muskat problem
-
MR2679821
-
- Absence of squirt singularities for the multi-phase Muskat problem, Comm. Math. Phys. 299 (2010), no. 2, 561–575. http://dx.doi.org/10.1007/s00220-010-1084-x. MR2679821
-
(2010)
Comm. Math. Phys.
, vol.299
, Issue.2
, pp. 561-575
-
-
Córdoba, D.1
Gancedo, F.2
-
14
-
-
84891391945
-
the confined Muskat problem: Differences with the deep water regime
-
MR3144991
-
D. CÓRDOBA, R. GRANERO-BELINCHÓN, and R. ORIVE-ILLERA, The confined Muskat problem: Differences with the deep water regime, Commun. Math. Sci. 12 (2014), no. 3, 423–455. http://dx.doi.org/10.4310/CMS.2014.v12.n3.a2. MR3144991
-
(2014)
Commun. Math. Sci.
, vol.12
, Issue.3
, pp. 423-455
-
-
Córdoba, D.1
Granero-Belinchón, R.2
Orive-Illera, R.3
-
15
-
-
84922362473
-
Steady-state fingering patterns for a periodic Muskat problem
-
MR3085780
-
M. EHRNSTRÖM, J. ESCHER, and B. V. MATIOC, Steady-state fingering patterns for a periodic Muskat problem, Methods Appl. Anal. 20 (2013), no. 1, 33–46. http://dx.doi.org/10.4310/MAA.2013.v20.n1.a2. MR3085780
-
(2013)
Methods Appl. Anal.
, vol.20
, Issue.1
, pp. 33-46
-
-
Ehrnström, M.1
Escher, J.2
Matioc, B.V.3
-
16
-
-
0039518556
-
the Dirichlet-Neumann operator on continuous functions
-
2, MR1288366
-
J. ESCHER, The Dirichlet-Neumann operator on continuous functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 21 (1994), no. 2, 235–266. MR1288366
-
(1994)
Ann. Scuola Norm. Sup. Pisa Cl. Sci.
, vol.21
, Issue.4
, pp. 235-266
-
-
Escher, J.1
-
17
-
-
84858405608
-
A generalized Rayleigh-Taylor condition for the Muskat problem
-
MR2864377
-
J. ESCHER, A. V. MATIOC, and B. V. MATIOC, A generalized Rayleigh-Taylor condition for the Muskat problem, Nonlinearity 25 (2012), no. 1, 73–92. http://dx.doi.org/10.1088/0951-7715/25/1/73. MR2864377
-
(2012)
Nonlinearity
, vol.25
, Issue.1
, pp. 73-92
-
-
Escher, J.1
Matioc, A.V.2
Matioc, B.V.3
-
18
-
-
73949124799
-
A moving boundary problem for periodic Stokesian Hele-Shaw flows
-
MR2487025
-
J. ESCHER and B. V. MATIOC, A moving boundary problem for periodic Stokesian Hele-Shaw flows, Interfaces Free Bound. 11 (2009), no. 1, 119–137. http://dx.doi.org/10.4171/IFB/205. MR2487025
-
(2009)
Interfaces Free Bound
, vol.11
, Issue.1
, pp. 119-137
-
-
Escher, J.1
Matioc, B.V.2
-
19
-
-
79953645127
-
on the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
-
MR2793001
-
- On the parabolicity of the Muskat problem: well-posedness, fingering, and stability results, Z. Anal. Anwend. 30 (2011), no. 2, 193–218. http://dx.doi.org/10.4171/ZAA/1431. MR2793001
-
(2011)
Z. Anal. Anwend.
, vol.30
, Issue.2
, pp. 193-218
-
-
Escher, J.1
Matioc, B.V.2
-
20
-
-
0000433754
-
Maximal regularity for a free boundary problem
-
MR1356871
-
J. ESCHER and G. SIMONETT, Maximal regularity for a free boundary problem, NoDEA Nonlinear Differential Equations Appl. 2 (1995), no. 4, 463–510. http://dx.doi.org/10.1007/BF01210620. MR1356871
-
(1995)
NoDEA Nonlinear Differential Equations Appl
, vol.2
, Issue.4
, pp. 463-510
-
-
Escher, J.1
Simonett, G.2
-
21
-
-
0031478022
-
Classical solutions of multidimensional Hele-Shaw models
-
MR1466667
-
- Classical solutions of multidimensional Hele-Shaw models, SIAM J. Math. Anal. 28 (1997), no. 5, 1028–1047. http://dx.doi.org/10.1137/S0036141095291919. MR1466667
-
(1997)
SIAM J. Math. Anal.
, vol.28
, Issue.5
, pp. 1028-1047
-
-
Escher, J.1
Simonett, G.2
-
22
-
-
84892595836
-
No-splash theorems for fluid interfaces
-
MR3181767
-
Ch. L. FEFFERMAN, No-splash theorems for fluid interfaces, Proc. Natl. Acad. Sci. USA 111 (2014), no. 2, 573–574. http://dx.doi.org/10.1073/pnas.1321805111. MR3181767
-
(2014)
Proc. Natl. Acad. Sci. USA
, vol.111
, Issue.2
, pp. 573-574
-
-
Fefferman, Ch.L.1
-
23
-
-
0037379124
-
Nonlinear stability of the Muskat problem with capillary pressure at the free boundary
-
MR1992404
-
A. FRIEDMAN and Y. TAO, Nonlinear stability of the Muskat problem with capillary pressure at the free boundary, Nonlinear Anal. 53 (2003), no. 1, 45–80. http://dx.doi.org/10.1016/S0362-546X(02)00286-9. MR1992404
-
(2003)
Nonlinear Anal
, vol.53
, Issue.1
, pp. 45-80
-
-
Friedman, A.1
Tao, Y.2
-
24
-
-
84892577446
-
Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem
-
MR3181769
-
F. GANCEDO and R. M. STRAIN, Absence of splash singularities for surface quasi-geostrophic sharp fronts and the Muskat problem, Proc. Natl. Acad. Sci. USA 111 (2014), no. 2, 635–639. http://dx.doi.org/10.1073/pnas.1320554111. MR3181769
-
(2014)
Proc. Natl. Acad. Sci. USA
, vol.111
, Issue.2
, pp. 635-639
-
-
Gancedo, F.1
Strain, R.M.2
-
25
-
-
0003549965
-
Elliptic partial differential equations of second order
-
Springer-Verlag, Berlin, Reprint of the 1998 edition. MR1814364
-
D. GILBARG and N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. MR1814364
-
(2001)
Classics in Mathematics
-
-
Gilbarg, D.1
Trudinger, N.S.2
-
26
-
-
84902663105
-
Global existence for the confined Muskat problem
-
MR3196945
-
R. GRANERO-BELINCHÓN, Global existence for the confined Muskat problem, SIAM J. Math. Anal. 46 (2014), no. 2, 1651–1680. http://dx.doi.org/10.1137/130912529. MR3196945
-
(2014)
SIAM J. Math. Anal.
, vol.46
, Issue.2
, pp. 1651-1680
-
-
Granero-Belinchón, R.1
-
27
-
-
0012489523
-
Muskat problem with surface tension
-
MR1471114
-
J. HONG, Y. TAO, and F. YI, Muskat problem with surface tension, J. Partial Differential Equations 10 (1997), no. 3, 213–231. MR1471114
-
(1997)
J. Partial Differential Equations
, vol.10
, Issue.3
, pp. 213-231
-
-
Hong, J.1
Tao, Y.2
Yi, F.3
-
28
-
-
84861461350
-
Elliptic operators and maximal regularity on periodic little-Hölder spaces
-
MR2923936
-
J. LECRONE, Elliptic operators and maximal regularity on periodic little-Hölder spaces, J. Evol. Equ. 12 (2012), no. 2, 295–325. http://dx.doi.org/10.1007/s00028-011-0133-z. MR2923936
-
(2012)
J. Evol. Equ.
, vol.12
, Issue.2
, pp. 295-325
-
-
Lecrone, J.1
-
29
-
-
0003963531
-
Analytic semigroups and optimal regularity in parabolic problems
-
Birkhäuser Verlag, Basel MR1329547
-
A. LUNARDI, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Progress in Nonlinear Differential Equations and their Applications, vol. 16, Birkhäuser Verlag, Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9234-6. MR1329547
-
(1995)
Progress in Nonlinear Differential Equations and Their Applications
, vol.16
-
-
Lunardi, A.1
-
30
-
-
0041755138
-
Two fluid systems in porous media: the encroachment of water into an oil sand
-
M. MUSKAT, Two fluid systems in porous media: The encroachment of water into an oil sand, Physics 5 (1934), no. 9, 250–264. http://dx.doi.org/10.1063/1.1745233.
-
(1934)
Physics
, vol.5
, Issue.9
, pp. 250-264
-
-
Muskat, M.1
-
31
-
-
0002500168
-
Equations d’évolution abstraites non linéaires de type parabolique
-
French, with English summary MR551075
-
G. DA PRATO and P. GRISVARD, Equations d’évolution abstraites non linéaires de type parabolique, Ann. Mat. Pura Appl. (4) 120 (1979), 329–396 (French, with English summary). http://dx.doi.org/10.1007/BF02411952. MR551075
-
(1979)
Ann. Mat. Pura Appl.
, vol.120
, Issue.4
, pp. 329-396
-
-
Prato, G.D.A.1
Grisvard, P.2
-
32
-
-
85010499164
-
Moving interfaces and quasilinear parabolic evolution equations
-
Birkhäuser/Springer, Cham MR3524106
-
J. PRÜSS and G. SIMONETT, Moving Interfaces and Quasilinear Parabolic Evolution Equations, Monographs in Mathematics, vol. 105, Birkhäuser/Springer, [Cham], 2016. http://dx.doi.org/10.1007/978-3-319-27698-4. MR3524106
-
(2016)
Monographs in Mathematics
, vol.105
-
-
Prüss, J.1
Simonett, G.2
-
33
-
-
85016703539
-
on the Muskat problem
-
MR3603251
-
- On the Muskat problem, Evol. Equ. Control Theory 5 (2016), no. 4, 631–645, available at http://arxiv.org/abs/arXiv:1606.03683v1.http://dx.doi.org/10.3934/eect.2016022. MR3603251
-
(2016)
Evol. Equ. Control Theory
, vol.5
, Issue.4
, pp. 631-645
-
-
Prüss, J.1
Simonett, G.2
-
34
-
-
0001383598
-
the penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
-
2 plates MR0097227
-
P. G. SAFFMAN and G. TAYLOR, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. Roy. Soc. London. Ser. A 245 (1958), 312–329. (2 plates). http://dx.doi.org/10.1098/rspa.1958.0085. MR0097227
-
(1958)
Proc. Roy. Soc. London. Ser. A
, vol.245
, pp. 312-329
-
-
Saffman, P.G.1
Taylor, G.2
-
35
-
-
4544228729
-
Global existence, singular solutions, and ill-posedness for the Muskat problem
-
MR2070208
-
M. SIEGEL, R. E. CAFLISCH, and S. HOWISON, Global existence, singular solutions, and ill-posedness for the Muskat problem, Comm. Pure Appl. Math. 57 (2004), no. 10, 1374–1411. http://dx.doi.org/10.1002/cpa.20040. MR2070208
-
(2004)
Comm. Pure Appl. Math.
, vol.57
, Issue.10
, pp. 1374-1411
-
-
Siegel, M.1
Caflisch, R.E.2
Howison, S.3
-
36
-
-
0004026738
-
-
2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, MR564653
-
A. E. TAYLOR and D. C. LAY, Introduction to Functional Analysis, 2nd ed., John Wiley & Sons, New York-Chichester-Brisbane, 1980. MR564653
-
(1980)
Introduction to Functional Analysis
-
-
Taylor, A.E.1
Lay, D.C.2
-
37
-
-
0348015444
-
Local classical solution of Muskat free boundary problem
-
MR1384001
-
F. YI, Local classical solution of Muskat free boundary problem, J. Partial Differential Equations 9 (1996), no. 1, 84–96. MR1384001
-
(1996)
J. Partial Differential Equations
, vol.9
, Issue.1
, pp. 84-96
-
-
Yi, F.1
-
38
-
-
0347604059
-
Global classical solution of Muskat free boundary problem
-
MR2019452
-
- Global classical solution of Muskat free boundary problem, J. Math. Anal. Appl. 288 (2003), no. 2, 442–461. http://dx.doi.org/10.1016/j.jmaa.2003.09.003. MR2019452
-
(2003)
J. Math. Anal. Appl.
, vol.288
, Issue.2
, pp. 442-461
-
-
Yi, F.1
-
39
-
-
84894905227
-
Stabilization of free surface flows in periodic porous media
-
MR3158474
-
M. WENZEL, Stabilization of free surface flows in periodic porous media, Nonlinear Anal. Real World Appl. 17 (2014), 265–282. http://dx.doi.org/10.1016/j.nonrwa.2013.12.004. MR3158474
-
(2014)
Nonlinear Anal. Real World Appl.
, vol.17
, pp. 265-282
-
-
Wenzel, M.1
|