-
1
-
-
79959880152
-
On the Cauchy problem for the water waves with surface tension
-
Alazard T., Burq N., Zuily C.: On the Cauchy problem for the water waves with surface tension. Duke Math. J. 158, 413-499 (2011).
-
(2011)
Duke Math. J.
, vol.158
, pp. 413-499
-
-
Alazard, T.1
Burq, N.2
Zuily, C.3
-
3
-
-
74949116792
-
Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves
-
Alazard T., Métivier G.: Paralinearization of the Dirichlet to Neumann operator, and regularity of three-dimensional water waves. Commun. Partial Differ. Equ. 34, 1632-1704 (2009).
-
(2009)
Commun. Partial Differ. Equ.
, vol.34
, pp. 1632-1704
-
-
Alazard, T.1
Métivier, G.2
-
4
-
-
38349102793
-
Large time existence for 3d water-waves and asymptotics
-
Alvarez-Samaniego B., Lannes D.: Large time existence for 3d water-waves and asymptotics. Invent. Math. 171, 485-541 (2008).
-
(2008)
Invent. Math.
, vol.171
, pp. 485-541
-
-
Alvarez-Samaniego, B.1
Lannes, D.2
-
5
-
-
1342266714
-
Well-posedness of vortex sheets with surface tension
-
Ambrose D.: Well-posedness of vortex sheets with surface tension. SIAM J. Math. Anal. 35, 211-244 (2003).
-
(2003)
SIAM J. Math. Anal.
, vol.35
, pp. 211-244
-
-
Ambrose, D.1
-
6
-
-
26944460000
-
The zero surface tension limit of two-dimensional water waves
-
Ambrose D. M., Masmoudi N.: The zero surface tension limit of two-dimensional water waves. Commun. Pure Appl. Math. 58, 1287-1315 (2005).
-
(2005)
Commun. Pure Appl. Math.
, vol.58
, pp. 1287-1315
-
-
Ambrose, D.M.1
Masmoudi, N.2
-
7
-
-
67249144683
-
The zero surface tension limit of three-dimensional water waves
-
Ambrose D. M., Masmoudi N.: The zero surface tension limit of three-dimensional water waves. Indiana Univ. Math. J. 58, 479-521 (2009).
-
(2009)
Indiana Univ. Math. J.
, vol.58
, pp. 479-521
-
-
Ambrose, D.M.1
Masmoudi, N.2
-
8
-
-
34547194744
-
Well-posedness of 3D vortex sheets with surface tension
-
Ambrose D., Masmoudi N.: Well-posedness of 3D vortex sheets with surface tension. Commun. Math. Sci. 5, 391-430 (2007).
-
(2007)
Commun. Math. Sci.
, vol.5
, pp. 391-430
-
-
Ambrose, D.1
Masmoudi, N.2
-
10
-
-
0031079899
-
Reappraisal of the KelvinHelmholtz problem. Part 1. Hamiltonian structure
-
Benjamin T. B., Bridges T. J.: Reappraisal of the KelvinHelmholtz problem. Part 1. Hamiltonian structure. J. Fluid Mech. 333, 301-325 (1997).
-
(1997)
J. Fluid Mech.
, vol.333
, pp. 301-325
-
-
Benjamin, T.B.1
Bridges, T.J.2
-
15
-
-
77950959732
-
On the limit as the density ratio tends to zero for two perfect incompressible 3-D fluids separated by a surface of discontinuity
-
Cheng A., Coutand D., Shkoller S.: On the limit as the density ratio tends to zero for two perfect incompressible 3-D fluids separated by a surface of discontinuity. Commun. Partial Differ. Equ. 35, 817-845 (2010).
-
(2010)
Commun. Partial Differ. Equ.
, vol.35
, pp. 817-845
-
-
Cheng, A.1
Coutand, D.2
Shkoller, S.3
-
16
-
-
0002988577
-
Fully nonlinear internal waves in a two-fluid system
-
Choi W., Camassa R.: Fully nonlinear internal waves in a two-fluid system. J. Fluid Mech. 396, 1-36 (1999).
-
(1999)
J. Fluid Mech.
, vol.396
, pp. 1-36
-
-
Choi, W.1
Camassa, R.2
-
17
-
-
78049501969
-
Strichartz estimates for the water-wave problem with surface tension
-
Christianson H., Hur V. M., Staffilani G.: Strichartz estimates for the water-wave problem with surface tension. Commun. Partial Differ. Equ. 35, 2195-2252 (2010).
-
(2010)
Commun. Partial Differ. Equ.
, vol.35
, pp. 2195-2252
-
-
Christianson, H.1
Hur, V.M.2
Staffilani, G.3
-
18
-
-
70350325132
-
Interface evolution: water waves in 2 - D
-
Cordoba A., Cordoba D., Gancedo F.: Interface evolution: water waves in 2 - D. Adv. Math. 223, 120-173 (2010).
-
(2010)
Adv. Math.
, vol.223
, pp. 120-173
-
-
Cordoba, A.1
Cordoba, D.2
Gancedo, F.3
-
19
-
-
34548446988
-
Well-posedness of the free-surface incompressible Euler equations with or without surface tension
-
Coutand D., Shkoller S.: Well-posedness of the free-surface incompressible Euler equations with or without surface tension. J. Am. Math. Soc. 20, 829-930 (2007).
-
(2007)
J. Am. Math. Soc.
, vol.20
, pp. 829-930
-
-
Coutand, D.1
Shkoller, S.2
-
20
-
-
0001688084
-
An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits
-
Craig W.: An existence theory for water waves and the Boussinesq and Korteweg-de Vries scaling limits. Commun. Partial Differ. Equ. 10, 787-1003 (1985).
-
(1985)
Commun. Partial Differ. Equ.
, vol.10
, pp. 787-1003
-
-
Craig, W.1
-
21
-
-
30544433668
-
Hamiltonian long-wave expansions for free surfaces and interfaces
-
Craig W., Guyenne P., Kalisch H.: Hamiltonian long-wave expansions for free surfaces and interfaces. Commun. Pure Appl. Math. 58, 1587-1641 (2005).
-
(2005)
Commun. Pure Appl. Math.
, vol.58
, pp. 1587-1641
-
-
Craig, W.1
Guyenne, P.2
Kalisch, H.3
-
22
-
-
0002686768
-
Numerical simulation of gravity waves
-
Craig W., Sulem C.: Numerical simulation of gravity waves. J. Comput. Phys. 108, 73-83 (1993).
-
(1993)
J. Comput. Phys.
, vol.108
, pp. 73-83
-
-
Craig, W.1
Sulem, C.2
-
24
-
-
0344453090
-
Ill-posedness of the Rayleigh-Taylor and Kelvin-Helmotz problems for incompressible fluids
-
Ebin G.: Ill-posedness of the Rayleigh-Taylor and Kelvin-Helmotz problems for incompressible fluids. Commun. Partial Differ. Equ. 13, 1265-1295 (1988).
-
(1988)
Commun. Partial Differ. Equ.
, vol.13
, pp. 1265-1295
-
-
Ebin, G.1
-
25
-
-
4344709446
-
Transmission problems and spectral theory for singular integral operators on Lipschitz domains
-
Escauriaza L., Mitrea M.: Transmission problems and spectral theory for singular integral operators on Lipschitz domains. J. Funct. Anal. 216, 141-171 (2004).
-
(2004)
J. Funct. Anal.
, vol.216
, pp. 141-171
-
-
Escauriaza, L.1
Mitrea, M.2
-
26
-
-
84857870242
-
Global solutions for the gravity water waves equation in dimension 3
-
Germain P., Masmoudi N., Shatah J.: Global solutions for the gravity water waves equation in dimension 3. Ann. Math. 175, 691-754 (2012).
-
(2012)
Ann. Math.
, vol.175
, pp. 691-754
-
-
Germain, P.1
Masmoudi, N.2
Shatah, J.3
-
27
-
-
0031503817
-
Pseudo-differential energy estimates of singular perturbations
-
Grenier E.: Pseudo-differential energy estimates of singular perturbations. Commun. Pure Appl. Math. 50, 821-865 (1997).
-
(1997)
Commun. Pure Appl. Math.
, vol.50
, pp. 821-865
-
-
Grenier, E.1
-
28
-
-
0032655167
-
Properties of large-amplitude internal waves
-
Grue J., Jensen A., Rusas P.-O., Sveen J. K.: Properties of large-amplitude internal waves. J. Fluid Mech. 380, 257-278 (1999).
-
(1999)
J. Fluid Mech.
, vol.380
, pp. 257-278
-
-
Grue, J.1
Jensen, A.2
Rusas, P.-O.3
Sveen, J.K.4
-
29
-
-
74849088012
-
Well-posedness of the Cauchy problem for models of large amplitude internal waves
-
Guyenne P., Lannes D., Saut J.-C.: Well-posedness of the Cauchy problem for models of large amplitude internal waves. Nonlinearity 23, 237-275 (2010).
-
(2010)
Nonlinearity
, vol.23
, pp. 237-275
-
-
Guyenne, P.1
Lannes, D.2
Saut, J.-C.3
-
31
-
-
0038473867
-
A nearly optimal existence result for slightly perturbed 3-D vortex sheets
-
Hou T. Y., Hu G.: A nearly optimal existence result for slightly perturbed 3-D vortex sheets. Commun. Partial Differ. Equ. 28, 155-198 (2003).
-
(2003)
Commun. Partial Differ. Equ.
, vol.28
, pp. 155-198
-
-
Hou, T.Y.1
Hu, G.2
-
32
-
-
33847163682
-
A long wave approximation for capillary-gravity waves and an effect of the bottom
-
Iguchi T.: A long wave approximation for capillary-gravity waves and an effect of the bottom. Commun. Partial Differ. Equ. 32, 37-85 (2007).
-
(2007)
Commun. Partial Differ. Equ.
, vol.32
, pp. 37-85
-
-
Iguchi, T.1
-
33
-
-
77950220771
-
A long wave approximation for capillary-gravity waves and the Kawahara equation
-
Iguchi T.: A long wave approximation for capillary-gravity waves and the Kawahara equation. Bull. Inst. Math. Acad. Sin. (N. S.) 2, 179-220 (2007).
-
(2007)
Bull. Inst. Math. Acad. Sin. (N.S.)
, vol.2
, pp. 179-220
-
-
Iguchi, T.1
-
34
-
-
69549128379
-
A shallow water approximation for water waves
-
Iguchi T.: A shallow water approximation for water waves. J. Math. Kyoto Univ. 49, 13-55 (2009).
-
(2009)
J. Math. Kyoto Univ.
, vol.49
, pp. 13-55
-
-
Iguchi, T.1
-
35
-
-
0031522531
-
On the two-phase free boundary problem for two-dimensional water waves
-
Iguchi T., Tanaka N., Tani A.: On the two-phase free boundary problem for two-dimensional water waves. Math. Ann. 309, 199-223 (1997).
-
(1997)
Math. Ann.
, vol.309
, pp. 199-223
-
-
Iguchi, T.1
Tanaka, N.2
Tani, A.3
-
36
-
-
17044418131
-
On 2D Rayleigh-Taylor instabilities
-
Kamotski V., Lebeau G.: On 2D Rayleigh-Taylor instabilities. Asymptot. Anal. 42, 1-27 (2005).
-
(2005)
Asymptot. Anal.
, vol.42
, pp. 1-27
-
-
Kamotski, V.1
Lebeau, G.2
-
37
-
-
0019633062
-
An investigation of internal solitary waves in a two-fluid system
-
Koop C. G., Butler G.: An investigation of internal solitary waves in a two-fluid system. J. Fluid Mech. 112, 225-251 (1981).
-
(1981)
J. Fluid Mech.
, vol.112
, pp. 225-251
-
-
Koop, C.G.1
Butler, G.2
-
38
-
-
11744344543
-
Nonlinear theory of the excitation of waves by a wind due to the Kelvin-Helmholtz instability
-
Kuznetsov E. A., Lushnikov P. L.: Nonlinear theory of the excitation of waves by a wind due to the Kelvin-Helmholtz instability. JETP 81, 332-340 (1995).
-
(1995)
Jetp
, vol.81
, pp. 332-340
-
-
Kuznetsov, E.A.1
Lushnikov, P.L.2
-
39
-
-
22544482964
-
Well-posedness of the water-waves equations
-
Lannes D.: Well-posedness of the water-waves equations. J. Am. Math. Soc. 18, 605-654 (2005).
-
(2005)
J. Am. Math. Soc.
, vol.18
, pp. 605-654
-
-
Lannes, D.1
-
40
-
-
31744440292
-
Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators
-
Lannes D.: Sharp estimates for pseudo-differential operators with symbols of limited smoothness and commutators. J. Funct. Anal. 232, 495-539 (2006).
-
(2006)
J. Funct. Anal.
, vol.232
, pp. 495-539
-
-
Lannes, D.1
-
41
-
-
84899790304
-
The water waves problem: mathematical analysis and asymptotics
-
AMS (in press)
-
Lannes, D.: The water waves problem: mathematical analysis and asymptotics. Mathematical Surveys and Monographs. AMS (in press).
-
Mathematical Surveys and Monographs
-
-
Lannes, D.1
-
42
-
-
17044425556
-
Régularité du problème de Kelvin-Helmholtz pour l'équation d'Euler 2d
-
Lebeau G.: Régularité du problème de Kelvin-Helmholtz pour l'équation d'Euler 2d. ESAIM: COCV 08(801-825), 08, 801-825 (2002).
-
(2002)
ESAIM: COCV
, vol.8
, Issue.801-825
, pp. 801-825
-
-
Lebeau, G.1
-
43
-
-
26044448758
-
Well-posedness for the motion of an incompressible liquid with free surface boundary
-
Lindblad, H.: Well-posedness for the motion of an incompressible liquid with free surface boundary. Ann. Math. (2)162, 109-194 (2005).
-
(2005)
Ann. Math.
, vol.162
, Issue.2
, pp. 109-194
-
-
Lindblad, H.1
-
44
-
-
71549133352
-
Well-posedness of the water-wave problem with surface tension
-
Ming M., Zhang Z.: Well-posedness of the water-wave problem with surface tension. J. Math. Pures Appl. 92, 429-455 (2009).
-
(2009)
J. Math. Pures Appl.
, vol.92
, pp. 429-455
-
-
Ming, M.1
Zhang, Z.2
-
45
-
-
0000306561
-
The Cauchy-Poisson problem (Russian), Dinamika Splosn. Sredy Vyp. 18 Dinamika Zidkost. so Svobod
-
Nalimov, V. I.: The Cauchy-Poisson problem (Russian), Dinamika Splosn. Sredy Vyp. 18 Dinamika Zidkost. so Svobod. Granicami 254, 104-210 (1974).
-
(1974)
Granicami
, vol.254
, pp. 104-210
-
-
Nalimov, V.I.1
-
46
-
-
48349100318
-
A Boussinesq system for two-way propagation of interfacial waves
-
Nguyen H. Y., Dias F.: A Boussinesq system for two-way propagation of interfacial waves. Physica D 237, 2365-2389 (2008).
-
(2008)
Physica D
, vol.237
, pp. 2365-2389
-
-
Nguyen, H.Y.1
Dias, F.2
-
47
-
-
62649143819
-
A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. Discrete Contin
-
Ohi K., Iguchi T.: A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. Discrete Contin. Dyn. Syst. 23, 1205-1240 (2009).
-
(2009)
Dyn. Syst.
, vol.23
, pp. 1205-1240
-
-
Ohi, K.1
Iguchi, T.2
-
48
-
-
0039742211
-
Cauchy problem in a scale of Banach spaces and its application to the shallow water theory justification
-
(Joint Sympos., IUTAM/IMU, Marseille, 1975)
-
Ovsjannikov, L. V.: Cauchy problem in a scale of Banach spaces and its application to the shallow water theory justification. In: Applications of Methods of Functional Analysis to Problems in Mechanics (Joint Sympos., IUTAM/IMU, Marseille, 1975), pp. 426-437. Lecture Notes in Mathematics, vol. 503. Springer, Berlin, 1976.
-
(1976)
Applications of Methods of Functional Analysis to Problems in Mechanics
, vol.503
, pp. 426-437
-
-
Ovsjannikov, L.V.1
-
50
-
-
79959970992
-
On the limit as the surface tension and density ratio tend to zero for the twophase Euler equations
-
Pusateri F.: On the limit as the surface tension and density ratio tend to zero for the twophase Euler equations. J. Hyperb. Differ. Equ. 8, 347-373 (2011).
-
(2011)
J. Hyperb. Differ. Equ.
, vol.8
, pp. 347-373
-
-
Pusateri, F.1
-
51
-
-
79954988210
-
Transverse instability of the line solitary water-waves
-
Rousset F., Tzvetkov N.: Transverse instability of the line solitary water-waves. Invent. Math. 184, 257-388 (2011).
-
(2011)
Invent. Math.
, vol.184
, pp. 257-388
-
-
Rousset, F.1
Tzvetkov, N.2
-
52
-
-
77953866714
-
On the transverse instability of one dimensional capillary-gravity waves
-
Rousset F., Tzvetkov N.: On the transverse instability of one dimensional capillary-gravity waves. DCDS-B 13, 859-872 (2010).
-
(2010)
Dcds-B
, vol.13
, pp. 859-872
-
-
Rousset, F.1
Tzvetkov, N.2
-
53
-
-
0036012969
-
The rigorous approximation of long-wavelength capillary-gravity waves
-
Schneider G., Wayne C. E.: The rigorous approximation of long-wavelength capillary-gravity waves. Arch. Ration. Mech. Anal. 162, 247-285 (2002).
-
(2002)
Arch. Ration. Mech. Anal.
, vol.162
, pp. 247-285
-
-
Schneider, G.1
Wayne, C.E.2
-
54
-
-
52349104032
-
Geometry and a priori estimates for free boundary problems of the Euler equation
-
Shatah J., Zeng C.: Geometry and a priori estimates for free boundary problems of the Euler equation. Commun. Pure Appl. Math. 61, 698-744 (2008).
-
(2008)
Commun. Pure Appl. Math.
, vol.61
, pp. 698-744
-
-
Shatah, J.1
Zeng, C.2
-
55
-
-
52349092767
-
A priori estimates for fluid interface problems
-
Shatah J., Zeng C.: A priori estimates for fluid interface problems. Commun. Pure Appl. Math. 61, 848-876 (2008).
-
(2008)
Commun. Pure Appl. Math.
, vol.61
, pp. 848-876
-
-
Shatah, J.1
Zeng, C.2
-
56
-
-
78751704957
-
Local well-posedness for fluid interface problems
-
Shatah J., Zeng C.: Local well-posedness for fluid interface problems. Arch. Ration. Mech. Anal. 199, 653-705 (2011).
-
(2011)
Arch. Ration. Mech. Anal.
, vol.199
, pp. 653-705
-
-
Shatah, J.1
Zeng, C.2
-
57
-
-
0004121498
-
Partial Differential Equations II: Qualitative Studies of Linear Equations
-
Springer, Berlin
-
Taylor, M. E.: Partial Differential Equations II: Qualitative Studies of Linear Equations. Applied Mathematical Sciences, vol. 116. Springer, Berlin, 1996.
-
(1996)
Applied Mathematical Sciences
, vol.116
-
-
Taylor, M.E.1
-
58
-
-
0003278083
-
Partial Differential Equations III
-
Springer, New York, Nonlinear Equations. Corrected reprint of the 1996 original
-
Taylor, M. E.: Partial Differential Equations III. Applied Mathematical Sciences, vol. 117. Springer, New York, 1997. Nonlinear Equations. Corrected reprint of the 1996 original.
-
(1997)
Applied Mathematical Sciences
, vol.117
-
-
Taylor, M.E.1
-
59
-
-
84968512992
-
Finite time analyticity for the two- and three-dimensional Rayleigh-Taylor instability
-
Sulem C., Sulem P.-L.: Finite time analyticity for the two- and three-dimensional Rayleigh-Taylor instability. Trans. Am. Math. Soc. 287, 127-160 (1981).
-
(1981)
Trans. Am. Math. Soc.
, vol.287
, pp. 127-160
-
-
Sulem, C.1
Sulem, P.-L.2
-
60
-
-
0038247451
-
Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability
-
Sulem C., Sulem P.-L., Bardos C., Frisch U.: Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability. Commun. Math. Phys. 80, 485-516 (1981).
-
(1981)
Commun. Math. Phys.
, vol.80
, pp. 485-516
-
-
Sulem, C.1
Sulem, P.-L.2
Bardos, C.3
Frisch, U.4
-
61
-
-
85045585725
-
Well-posedeness in Sobolev spaces of the full water wave problem in 2-D
-
Wu S.: Well-posedeness in Sobolev spaces of the full water wave problem in 2-D. Invent. Math. 130, 439-472 (1997).
-
(1997)
Invent. Math.
, vol.130
, pp. 439-472
-
-
Wu, S.1
-
62
-
-
0033446356
-
Well-posedness in Sobolev spaces of the full water wave problem in 3-D
-
Wu S.: Well-posedness in Sobolev spaces of the full water wave problem in 3-D. J. Am. Math. Soc. 12, 445-495 (1999).
-
(1999)
J. Am. Math. Soc.
, vol.12
, pp. 445-495
-
-
Wu, S.1
-
63
-
-
33745626744
-
Mathematical analysis of vortex sheets
-
Wu S.: Mathematical analysis of vortex sheets. Commun. Pure Appl. Math. 59, 1065-1206 (2006).
-
(2006)
Commun. Pure Appl. Math.
, vol.59
, pp. 1065-1206
-
-
Wu, S.1
-
64
-
-
67650433790
-
Almost global wellposedness of the 2-D full water wave problem
-
Wu S.: Almost global wellposedness of the 2-D full water wave problem. Invent. Math. 177, 45-135 (2009).
-
(2009)
Invent. Math.
, vol.177
, pp. 45-135
-
-
Wu, S.1
-
65
-
-
79952989811
-
Global well-posedness of the 3-D full water wave problem
-
Wu S.: Global well-posedness of the 3-D full water wave problem. Invent. Math. 184, 125-220 (2011).
-
(2011)
Invent. Math.
, vol.184
, pp. 125-220
-
-
Wu, S.1
-
66
-
-
85009585833
-
Gravity waves on the free surface of an incompressible perfect fluid of finite depth
-
Yosihara H.: Gravity waves on the free surface of an incompressible perfect fluid of finite depth. Publ. Res. Inst. Math. Sci. 18, 49-96 (1982).
-
(1982)
Publ. Res. Inst. Math. Sci.
, vol.18
, pp. 49-96
-
-
Yosihara, H.1
-
67
-
-
0000375767
-
Capillary-gravity waves for an incompressible ideal fluid
-
Yosihara H.: Capillary-gravity waves for an incompressible ideal fluid. J. Math. Kyoto Univ. 23, 649-694 (1983).
-
(1983)
J. Math. Kyoto Univ.
, vol.23
, pp. 649-694
-
-
Yosihara, H.1
-
68
-
-
34250447917
-
Stability of periodic waves of nite amplitude on the surface of a deep fluid
-
Zakharov V. E.: Stability of periodic waves of nite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 9, 190-194 (1968).
-
(1968)
J. Appl. Mech. Tech. Phys.
, vol.9
, pp. 190-194
-
-
Zakharov, V.E.1
|