-
1
-
-
33749026600
-
The flow of water
-
Hele-Shaw (1898) The flow of water. Nature 58:34-36.
-
(1898)
Nature
, vol.58
, pp. 34-36
-
-
Hele-Shaw1
-
2
-
-
0001383598
-
The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
-
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.
-
(1958)
Proc R Soc London Ser A
, vol.245
, pp. 312-329
-
-
Saffman, P.-G.1
Taylor, G.2
-
5
-
-
0002418219
-
The instability of liquid surfaces when accelerated in a direction perpendicular to their planes
-
Taylor G (1950) The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc R Soc Lond Ser A 201:192-196.
-
(1950)
Proc R Soc Lond Ser A
, vol.201
, pp. 192-196
-
-
Taylor, G.1
-
6
-
-
84990576574
-
Growth rates for the linearized motion of fluid interfaces away from equilibrium
-
Beale T, Hou T, Lowengrub J (1993) Growth rates for the linearized motion of fluid interfaces away from equilibrium. Commun Pure Appl Math 46:1269-1301.
-
(1993)
Commun Pure Appl Math
, vol.46
, pp. 1269-1301
-
-
Beale, T.1
Hou, T.2
Lowengrub, J.3
-
7
-
-
0031506263
-
Well-posedness in Sobolev spaces of the full water wave problem in 2-D
-
Wu S (1997) Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent Math 130:39-72.
-
(1997)
Invent Math
, vol.130
, pp. 39-72
-
-
Wu, S.1
-
8
-
-
0033446356
-
Well-posedness in Sobolev spaces of the full water wave problem in 3-D
-
Wu S (1999) Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J Am Math Soc 12:445-495.
-
(1999)
J Am Math Soc
, vol.12
, pp. 445-495
-
-
Wu, S.1
-
9
-
-
0034368951
-
On the motion of the free surface of a liquid
-
Christodoulou D, Lindblad H (2000) On the motion of the free surface of a liquid. Comm Pure Appl Math 53:1536-1602.
-
(2000)
Comm Pure Appl Math
, vol.53
, pp. 1536-1602
-
-
Christodoulou, D.1
Lindblad, H.2
-
10
-
-
16644399272
-
Well-posedness of two-phase Hele-Shaw Flow without surface tension
-
Ambrose D (2004) Well-posedness of two-phase Hele-Shaw Flow without surface tension. Eur J Appl Math 15:597-607.
-
(2004)
Eur J Appl Math
, vol.15
, pp. 597-607
-
-
Ambrose, D.1
-
11
-
-
26044448758
-
Well-posedness for the motion of an incompressible liquid with free surface boundary
-
Lindblad H (2005) Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann Math 162:109-194.
-
(2005)
Ann Math
, vol.162
, pp. 109-194
-
-
Lindblad, H.1
-
12
-
-
26944460000
-
The zero surface tension limit of two-dimensional water waves
-
Ambrose D, Masmoudi N (2005) The zero surface tension limit of two-dimensional water waves. Commun Pure Appl Math 58:1287-1315.
-
(2005)
Commun Pure Appl Math
, vol.58
, pp. 1287-1315
-
-
Ambrose, D.1
Masmoudi, N.2
-
13
-
-
34548446988
-
Well-posedness of the free-surface incompressible Euler equations with or without surface tension
-
Coutand D, Shkoller S (2007)Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J Am Math Soc 20:829-930.
-
(2007)
J Am Math Soc
, vol.20
, pp. 829-930
-
-
Coutand, D.1
Shkoller, S.2
-
14
-
-
34249881893
-
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 273:445-471.
-
(2007)
Commun Math Phys
, vol.273
, pp. 445-471
-
-
Córdoba, D.1
Gancedo, F.2
-
15
-
-
52349104032
-
Geometry and a priori estimates for free boundary problems of the Euler equation
-
Shatah J, Zeng C (2008) Geometry and a priori estimates for free boundary problems of the Euler equation. Commun Pure Appl Math 61:698-744.
-
(2008)
Commun Pure Appl Math
, vol.61
, pp. 698-744
-
-
Shatah, J.1
Zeng, C.2
-
16
-
-
52349109943
-
On the free boundary problem of three-dimensional incompressible euler equations
-
Zhang P, Zhang Z (2008) On the free boundary problem of three-dimensional incompressible euler equations. Commun Pure Appl Math 61:877-940.
-
(2008)
Commun Pure Appl Math
, vol.61
, pp. 877-940
-
-
Zhang, P.1
Zhang, Z.2
-
17
-
-
79551566131
-
Interface evolution: The Hele-Shaw and Muskat problems
-
in press
-
Córdoba A, Córdoba D, Gancedo F (2009) Interface evolution: The Hele-Shaw and Muskat problems. Ann Math, in press.
-
(2009)
Ann Math
-
-
Córdoba, A.1
Córdoba, D.2
Gancedo, F.3
-
18
-
-
67650365418
-
-
Córdoba A, Córdoba D, Gancedo F (2008) Interface evolution: The water wave problem in 2D. arXiv:0810.5340v1 [math.AP].
-
Córdoba A, Córdoba D, Gancedo F (2008) Interface evolution: The water wave problem in 2D. arXiv:0810.5340v1 [math.AP].
-
-
-
-
19
-
-
0011555392
-
The equations of motion of a perfect fluid with free boundary are not well posed
-
Ebin D-G (1987) The equations of motion of a perfect fluid with free boundary are not well posed. Commun Partial Differential Equations 12:1175-1201.
-
(1987)
Commun Partial Differential Equations
, vol.12
, pp. 1175-1201
-
-
Ebin, D.-G.1
-
20
-
-
0344453090
-
Ill-posedness of the Rayleigh-Taylor and Helmholtz problems for incompressible fluids
-
Ebin D-G (1988) Ill-posedness of the Rayleigh-Taylor and Helmholtz problems for incompressible fluids. Commun Partial Differential Equations 13: 1265-1295.
-
(1988)
Commun Partial Differential Equations
, vol.13
, pp. 1265-1295
-
-
Ebin, D.-G.1
-
21
-
-
0001747831
-
Singular solutions and ill-posedness for the evolution of vortex sheets
-
Caflisch R, Orellana O (1989) Singular solutions and ill-posedness for the evolution of vortex sheets. SIAM J Math Anal 20:293-307.
-
(1989)
SIAM J Math Anal
, vol.20
, pp. 293-307
-
-
Caflisch, R.1
Orellana, O.2
-
22
-
-
4544228729
-
Global existence, singular solutions, and ill-posedness for the Muskat problem
-
Siegel M, Caflisch R, Howison S (2004) Global existence, singular solutions, and ill-posedness for the Muskat problem. Commun Pure Appl Math 57:1374-1411.
-
(2004)
Commun Pure Appl Math
, vol.57
, pp. 1374-1411
-
-
Siegel, M.1
Caflisch, R.2
Howison, S.3
-
23
-
-
0008283862
-
Removing the stiffness from interfacial flows with surface tension
-
Hou T, Lowengrub J, Shelley M (1994) Removing the stiffness from interfacial flows with surface tension. J Comput Phys 114:312-338.
-
(1994)
J Comput Phys
, vol.114
, pp. 312-338
-
-
Hou, T.1
Lowengrub, J.2
Shelley, M.3
-
24
-
-
39749086442
-
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.
-
(2008)
Adv Math
, vol.217
, pp. 2569-2598
-
-
Gancedo, F.1
-
25
-
-
0004136765
-
-
Princeton Univ Press, Princeton, NJ
-
Stein E (1993) Harmonic Analysis (Princeton Univ Press, Princeton, NJ).
-
(1993)
Harmonic Analysis
-
-
Stein, E.1
-
26
-
-
0020191249
-
Generalized vortex methods for free-surface flow problems
-
Baker G, Meiron D, Orszag S (1982) Generalized vortex methods for free-surface flow problems. J Fluid Mech 123:477-501.
-
(1982)
J Fluid Mech
, vol.123
, pp. 477-501
-
-
Baker, G.1
Meiron, D.2
Orszag, S.3
-
27
-
-
33646697141
-
Phase transitions: Uniform regularity of the intermediate layers
-
Caffarelli L-A, Córdoba A (2006) Phase transitions: Uniform regularity of the intermediate layers. J Reine Angew Math 593:209-235.
-
(2006)
J Reine Angew Math
, vol.593
, pp. 209-235
-
-
Caffarelli, L.-A.1
Córdoba, A.2
-
29
-
-
4544377751
-
A maximum principle applied to quasi-geostrophic equations
-
Córdoba A, Córdoba D (2004) A maximum principle applied to quasi-geostrophic equations. Commun Math Phys 249:511-528.
-
(2004)
Commun Math Phys
, vol.249
, pp. 511-528
-
-
Córdoba, A.1
Córdoba, D.2
|