no. 6
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) no. 6, pp. 753-781 
@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},
     pages = {753--781},
     year = {2005},
     publisher = {Elsevier},
     volume = {22},
     number = {6},
     doi = {10.1016/j.anihpc.2004.11.001},
     mrnumber = {2172858},
     zbl = {02245285},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.11.001/}
}
TY  - JOUR
AU  - Schweizer, Ben
TI  - On the three-dimensional Euler equations with a free boundary subject to surface tension
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2005
SP  - 753
EP  - 781
VL  - 22
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2004.11.001/
DO  - 10.1016/j.anihpc.2004.11.001
LA  - en
ID  - AIHPC_2005__22_6_753_0
ER  - 
%0 Journal Article
%A Schweizer, Ben
%T On the three-dimensional Euler equations with a free boundary subject to surface tension
%J Annales de l'I.H.P. Analyse non linéaire
%D 2005
%P 753-781
%V 22
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2004.11.001/
%R 10.1016/j.anihpc.2004.11.001
%G en
%F 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) no. 6, pp. 753-781. doi: 10.1016/j.anihpc.2004.11.001

[1] Beale J.T., Large time regularity of viscous surface waves, Arch. Rat. Mech. Anal. 84 (1984) 307-352. | Zbl | MR

[2] Beyer K., Günther M., On the Cauchy problem for a capillary drop. I. Irrotational motion, Math. Methods Appl. Sci. 21 (12) (1998) 1149-1183. | Zbl | MR

[3] Chen X., Friedman A., A bubble in ideal fluid with gravity, J. Differential Equations 81 (1989) 136-166. | Zbl | MR

[4] Christodoulou D., Lindblad H., On the motion of the free surface of a liquid, Comm. Pure Appl. Math. 53 (12) (2000) 1536-1602. | Zbl | MR

[5] Ebin D.G., The equations of motion of a perfect fluid with free boundary are not well posed, Comm. Partial Differential Equations 12 (1987) 1175-1201. | Zbl | MR

[6] Evans L.C., Partial Differential Equations, Grad. Stud. Math., vol. 19, Amer. Math. Soc., 1998. | Zbl | MR

[7] Iguchi T., Tanaka N., Tani A., On the two-phase free boundary problem for two-dimensional water waves, Math. Ann. 309 (2) (1997) 199-223. | Zbl | MR

[8] Iguchi T., Tanaka N., Tani A., On a free boundary problem for an incompressible ideal fluid in two space dimensions, Adv. Math. Sci. Appl. 9 (1) (1999) 415-472. | Zbl | MR

[9] Kato T., Ponce G., Well-posedness of the Euler and Navier-Stokes equations in Lebesgue spaces, Rev. Mat. Iberoamericana 2 (1986) 73-88. | Zbl | MR

[10] Lions J.L., Magenes E., Non-Homogeneous Boundary Value Problems and Applications, I, Grundlehren Math. Wiss., vol. 181, Springer-Verlag, 1972. | Zbl

[11] Ogawa M., Tani A., Free boundary problem for an incompressible ideal fluid with surface tension, Math. Models Methods Appl. Sci. 12 (12) (2002) 1725-1740. | Zbl | MR

[12] Okazawa N., The Euler equation on a bounded domain as a quasilinear evolution equation, Commun. Appl. Nonlinear Anal. 3 (3) (1996) 107-113. | Zbl | MR

[13] Renardy M., An existence theorem for a free surface flow problem with open boundaries, Comm. Partial Differential Equations 17 (1992) 1387-1405. | Zbl | MR

[14] Schweizer B., A two-component flow with a viscous and an inviscid fluid, Comm. Partial Differential Equations 25 (2000) 887-901. | Zbl | MR

[15] Triebel H., Theory of Function Spaces, Monographs Math., vol. 78, Birkhäuser, 1983. | Zbl | MR

[16] Triebel H., Theory of Function Spaces II, Monographs Math., vol. 84, Birkhäuser, 1992. | Zbl | MR

[17] Wagner A., On the Bernoulli free boundary problem with surface tension, in: Athanasopoulos I. (Ed.), Free boundary problems: theory and applications, CRC Res. Notes Math., vol. 409, Chapman & Hall, 1999, pp. 246-251. | Zbl | MR

[18] Wu S., Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math. 130 (1) (1997) 39-72. | Zbl | MR

[19] Wu S., Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc. 12 (2) (1999) 445-495. | Zbl | MR

Cité par Sources :