@article{AIHPC_2005__22_6_753_0, author = {Schweizer, Ben}, title = {On the three-dimensional Euler equations with a free boundary subject to surface tension}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {22}, year = {2005}, pages = {753-781}, doi = {10.1016/j.anihpc.2004.11.001}, mrnumber = {2172858}, zbl = {02245285}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2005__22_6_753_0} }
Schweizer, Ben. On the three-dimensional Euler equations with a free boundary subject to surface tension. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) pp. 753-781. doi : 10.1016/j.anihpc.2004.11.001. http://gdmltest.u-ga.fr/item/AIHPC_2005__22_6_753_0/
[1] Large time regularity of viscous surface waves, Arch. Rat. Mech. Anal. 84 (1984) 307-352. | MR 721189 | Zbl 0545.76029
,[2] On the Cauchy problem for a capillary drop. I. Irrotational motion, Math. Methods Appl. Sci. 21 (12) (1998) 1149-1183. | MR 1637554 | Zbl 0916.35141
, ,[3] A bubble in ideal fluid with gravity, J. Differential Equations 81 (1989) 136-166. | MR 1012203 | Zbl 0686.35111
, ,[4] On the motion of the free surface of a liquid, Comm. Pure Appl. Math. 53 (12) (2000) 1536-1602. | MR 1780703 | Zbl 1031.35116
, ,[5] The equations of motion of a perfect fluid with free boundary are not well posed, Comm. Partial Differential Equations 12 (1987) 1175-1201. | MR 886344 | Zbl 0631.76018
,[6] Partial Differential Equations, Grad. Stud. Math., vol. 19, Amer. Math. Soc., 1998. | MR 1625845 | Zbl 0902.35002
,[7] On the two-phase free boundary problem for two-dimensional water waves, Math. Ann. 309 (2) (1997) 199-223. | MR 1474190 | Zbl 0897.76017
, , ,[8] On a free boundary problem for an incompressible ideal fluid in two space dimensions, Adv. Math. Sci. Appl. 9 (1) (1999) 415-472. | MR 1690447 | Zbl 0951.76011
, , ,[9] Well-posedness of the Euler and Navier-Stokes equations in Lebesgue spaces, Rev. Mat. Iberoamericana 2 (1986) 73-88. | MR 864654 | Zbl 0615.35078
, ,[10] Non-Homogeneous Boundary Value Problems and Applications, I, Grundlehren Math. Wiss., vol. 181, Springer-Verlag, 1972. | Zbl 0223.35039
, ,[11] Free boundary problem for an incompressible ideal fluid with surface tension, Math. Models Methods Appl. Sci. 12 (12) (2002) 1725-1740. | MR 1946720 | Zbl 1023.76007
, ,[12] The Euler equation on a bounded domain as a quasilinear evolution equation, Commun. Appl. Nonlinear Anal. 3 (3) (1996) 107-113. | MR 1397596 | Zbl 0859.35100
,[13] An existence theorem for a free surface flow problem with open boundaries, Comm. Partial Differential Equations 17 (1992) 1387-1405. | MR 1179291 | Zbl 0767.35061
,[14] A two-component flow with a viscous and an inviscid fluid, Comm. Partial Differential Equations 25 (2000) 887-901. | MR 1759796 | Zbl 0955.35062
,[15] Theory of Function Spaces, Monographs Math., vol. 78, Birkhäuser, 1983. | MR 781540 | Zbl 0546.46027
,[16] Theory of Function Spaces II, Monographs Math., vol. 84, Birkhäuser, 1992. | MR 1163193 | Zbl 0778.46022 | Zbl 0763.46025
,[17] On the Bernoulli free boundary problem with surface tension, in: (Ed.), Free boundary problems: theory and applications, CRC Res. Notes Math., vol. 409, Chapman & Hall, 1999, pp. 246-251. | MR 1708476 | Zbl 0930.35139
,[18] Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math. 130 (1) (1997) 39-72. | MR 1471885 | Zbl 0892.76009
,[19] Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc. 12 (2) (1999) 445-495. | MR 1641609 | Zbl 0921.76017
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