-
1
-
-
16644399272
-
Well-posedness of two-phase Hele-Shaw flow without surface tension
-
D. M. Ambrose, Well-posedness of two-phase Hele-Shaw flow without surface tension, European J. Appl. Math. 15 (2004), 597-607.
-
(2004)
European J. Appl. Math.
, vol.15
, pp. 597-607
-
-
Ambrose, D.M.1
-
4
-
-
1542680901
-
Convergence of a boundary integral method for water waves
-
J. T. Beale, T. Y. Hou, and J. Lowengrub, Convergence of a boundary integral method for water waves, SIAM J. Numer. Anal. 33 (1996), 1797-1843.
-
(1996)
SIAM J. Numer. Anal.
, vol.33
, pp. 1797-1843
-
-
Beale, J.T.1
Hou, T.Y.2
Lowengrub, J.3
-
5
-
-
84857702350
-
-
preprint
-
A. Castro, D. Córdoba, C. L. Fefferman, and F. Gancedo, Breakdown of smoothness for the Muskat problem, 2011, preprint.
-
(2011)
Breakdown of smoothness for the Muskat problem
-
-
Castro, A.1
Córdoba, D.2
Fefferman, C.L.3
Gancedo, F.4
-
6
-
-
79953190074
-
Turning waves and breakdown for incompressible flows
-
A. Castro, D. Córdoba, C. L. Fefferman, F. Gancedo, and M. López-Fernández, Turning waves and breakdown for incompressible flows, Proc. Natl. Acad. Sci. USA 108 (2011), 4754-4759.
-
(2011)
Proc. Natl. Acad. Sci. USA
, vol.108
, pp. 4754-4759
-
-
Castro, A.1
Córdoba, D.2
Fefferman, C.L.3
Gancedo, F.4
López-Fernández, M.5
-
7
-
-
0000985293
-
Wave breaking for nonlinear nonlocal shallow water equations
-
A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math. 181 (1998), 229-243.
-
(1998)
Acta Math
, vol.181
, pp. 229-243
-
-
Constantin, A.1
Escher, J.2
-
8
-
-
84870705750
-
-
to appear in JEMS
-
P. Constantin, D. Córdoba, F. Gancedo, and R. Strain, On the global existence for the Muskat problem, 2012, to appear in JEMS.
-
(2012)
On the global existence for the Muskat problem
-
-
Constantin, P.1
Córdoba, D.2
Gancedo, F.3
Strain, R.4
-
9
-
-
0000851461
-
Global solutions for small data to the Hele-Shaw problem
-
P. Constantin and M. Pugh, Global solutions for small data to the Hele-Shaw problem, Nonlinearity 6 (1993), 393-415.
-
(1993)
Nonlinearity
, vol.6
, pp. 393-415
-
-
Constantin, P.1
Pugh, M.2
-
10
-
-
0346734144
-
A pointwise estimate for fractionary derivatives with applications to partial differential equations
-
A. Córdoba and D. Córdoba, A pointwise estimate for fractionary derivatives with applications to partial differential equations, Proc. Natl. Acad. Sci. USA 100 (2003), 15316-15317.
-
(2003)
Proc. Natl. Acad. Sci. USA
, vol.100
, pp. 15316-15317
-
-
Córdoba, A.1
Córdoba, D.2
-
11
-
-
70350325132
-
Interface evolution: water waves in 2-D
-
A. Córdoba, D. Córdoba, and F. Gancedo, Interface evolution: water waves in 2-D, Adv. Math. 223 (2010), 120-173.
-
(2010)
Adv. Math.
, vol.223
, pp. 120-173
-
-
Córdoba, A.1
Córdoba, D.2
Gancedo, F.3
-
12
-
-
78751624212
-
Interface evolution: the Hele-Shaw and Muskat problems
-
A. Córdoba, Interface evolution: the Hele-Shaw and Muskat problems, Ann. of Math. 173 (2011), 477-542.
-
(2011)
Ann. of Math.
, vol.173
, pp. 477-542
-
-
Córdoba, A.1
-
13
-
-
34249881893
-
Contour dynamics of incompressible 3-D flu-ids in a porous medium with different densities
-
D. Córdoba and F. Gancedo, Contour dynamics of incompressible 3-D flu-ids in a porous medium with different densities, Comm. Math. Phys. 273 (2007), 445-471.
-
(2007)
Comm. Math. Phys.
, vol.273
, pp. 445-471
-
-
Córdoba, D.1
Gancedo, F.2
-
14
-
-
58849109361
-
A maximum principle for the Muskat problem for fluids with different densities
-
D. Córdoba and F. Gancedo, A maximum principle for the Muskat problem for fluids with different densities, Comm. Math. Phys. 286 (2009), 681-696.
-
(2009)
Comm. Math. Phys.
, vol.286
, pp. 681-696
-
-
Córdoba, D.1
Gancedo, F.2
-
15
-
-
77955845839
-
Absence of squirt singularities for the multi-phase Muskat problem
-
D. Córdoba and F. Gancedo, Absence of squirt singularities for the multi-phase Muskat problem, Comm. Math. Phys. 299 (2010), 561-575.
-
(2010)
Comm. Math. Phys.
, vol.299
, pp. 561-575
-
-
Córdoba, D.1
Gancedo, F.2
-
16
-
-
44649179813
-
A note on interface dynamics for convection in porous media
-
D. Córdoba, F. Gancedo, and R. Orive, A note on interface dynamics for convection in porous media, Phys. D 237 (2008), 1488-1497.
-
(2008)
Phys. D
, vol.237
, pp. 1488-1497
-
-
Córdoba, D.1
Gancedo, F.2
Orive, R.3
-
17
-
-
0024720053
-
Contour dynamics and contour surgery: numerical algorithms for extended, high-resolution modelling of vortex dynamics in two-dimensional, inviscid, incompressible flows
-
D. G. Dritschel, Contour dynamics and contour surgery: numerical algorithms for extended, high-resolution modelling of vortex dynamics in two-dimensional, inviscid, incompressible flows, Comput. Phys. Rep. 10 (1989), 77-146.
-
(1989)
Comput. Phys. Rep.
, vol.10
, pp. 77-146
-
-
Dritschel, D.G.1
-
19
-
-
79953645127
-
On the parabolicity of the Muskat problem: well-posedness, fingering, and stability results
-
J. Escher and B.-V. Matioc, 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.-V.2
-
20
-
-
0000010015
-
Classical solutions for Hele-Shaw models with surface tension
-
J. Escher and G. Simonett, Classical solutions for Hele-Shaw models with surface tension, Adv. Differential Equations 2 (1997), 619-642.
-
(1997)
Adv. Differential Equations
, vol.2
, pp. 619-642
-
-
Escher, J.1
Simonett, G.2
-
21
-
-
0004317158
-
-
Springer-Verlag, New York
-
E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations. I. Nonstiff problems, Springer Ser. Comput. Math. 8, Springer-Verlag, New York, 1987.
-
(1987)
Solving Ordinary Differential Equations. I. Nonstiff problems, Springer Ser. Comput. Math
, vol.8
-
-
Hairer, E.1
Nørsett, S.P.2
Wanner, G.3
-
22
-
-
0345415372
-
On the motion of a viscous fluid between two parallel plates
-
Hele-Shaw
-
Hele-Shaw, On the motion of a viscous fluid between two parallel plates, Trans. Royal Inst. Nav. Archit. 40,21 (1989).
-
(1989)
Trans. Royal Inst. Nav. Archit.
, vol.40
, pp. 21
-
-
-
23
-
-
0008283862
-
Removing the stiffness from interfacial flows with surface tension
-
T. Y. Hou, J. S. Lowengrub, and M. J. Shelley, Removing the stiffness from interfacial flows with surface tension, J. Comput. Phys. 114 (1994), 312-338.
-
(1994)
J. Comput. Phys.
, vol.114
, pp. 312-338
-
-
Hou, T.Y.1
Lowengrub, J.S.2
Shelley, M.J.3
-
25
-
-
0041033033
-
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), 250-264.
-
(1934)
Physics
, vol.5
, pp. 250-264
-
-
Muskat, M.1
-
26
-
-
84972536320
-
An abstract form of the nonlinear Cauchy-Kowalewski theorem
-
L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry 6 (1972), 561-576.
-
(1972)
J. Differential Geometry
, vol.6
, pp. 561-576
-
-
Nirenberg, L.1
-
27
-
-
84972513394
-
A note on a theorem of Nirenberg
-
T. Nishida, A note on a theorem of Nirenberg, J. Differential Geom. 12 (1977), 629-633 (1978).
-
(1978)
J. Differential Geom.
, vol.12
, Issue.1977
, pp. 629-633
-
-
Nishida, T.1
-
28
-
-
0031211418
-
Viscous fingering: an optimal bound on the growth rate of the mixing zone
-
F. Otto, Viscous fingering: an optimal bound on the growth rate of the mixing zone, SIAM J. Appl. Math. 57 (1997), 982-990.
-
(1997)
SIAM J. Appl. Math.
, vol.57
, pp. 982-990
-
-
Otto, F.1
-
30
-
-
0001383598
-
The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
-
(2 plates)
-
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).
-
(1958)
Proc. Roy. Soc. London. Ser. A
, vol.245
, pp. 312-329
-
-
Saffman, P.G.1
Taylor, G.2
-
31
-
-
4544228729
-
Global existence, singular solutions, and ill-posedness for the Muskat problem
-
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), 1374-1411.
-
(2004)
Comm. Pure Appl. Math.
, vol.57
, pp. 1374-1411
-
-
Siegel, M.1
Caflisch, R.E.2
Howison, S.3
-
32
-
-
0038247451
-
Finite time analyticity for the two-and three-dimensional Kelvin-Helmholtz instability
-
C. Sulem, P.-L. Sulem, C. Bardos, and U. Frisch, Finite time analyticity for the two-and three-dimensional Kelvin-Helmholtz instability, Comm. Math. Phys. 80 (1981), 485-516.
-
(1981)
Comm. Math. Phys.
, vol.80
, pp. 485-516
-
-
Sulem, C.1
Sulem, P.-L.2
Bardos, C.3
Frisch, U.4
-
33
-
-
0348015444
-
Local classical solution of Muskat free boundary problem
-
F. Yi, Local classical solution of Muskat free boundary problem, J. Partial Differential Equations 9 (1996), 84-96.
-
(1996)
J. Partial Differential Equations
, vol.9
, pp. 84-96
-
-
Yi, F.1
-
34
-
-
0347604059
-
Global classical solution of Muskat free boundary problem
-
F. Yi, Global classical solution of Muskat free boundary problem, J. Math. Anal. Appl. 288 (2003), 442-461.
-
(2003)
J. Math. Anal. Appl.
, vol.288
, pp. 442-461
-
-
Yi, F.1
|