On the three-dimensional Euler equations with a free boundary subject to surface tension

Ben Schweizer

Annales de l'I.H.P. Analyse non linéaire (2005)

  • Volume: 22, Issue: 6, page 753-781
  • ISSN: 0294-1449

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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 22.6 (2005): 753-781. <http://eudml.org/doc/78677>.

@article{Schweizer2005,
author = {Schweizer, Ben},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {three-dimensional Euler equations; free boundary},
language = {eng},
number = {6},
pages = {753-781},
publisher = {Elsevier},
title = {On the three-dimensional Euler equations with a free boundary subject to surface tension},
url = {http://eudml.org/doc/78677},
volume = {22},
year = {2005},
}

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
PB - Elsevier
VL - 22
IS - 6
SP - 753
EP - 781
LA - eng
KW - three-dimensional Euler equations; free boundary
UR - http://eudml.org/doc/78677
ER -

References

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  1. [1] Beale J.T., Large time regularity of viscous surface waves, Arch. Rat. Mech. Anal.84 (1984) 307-352. Zbl0545.76029MR721189
  2. [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. Zbl0916.35141MR1637554
  3. [3] Chen X., Friedman A., A bubble in ideal fluid with gravity, J. Differential Equations81 (1989) 136-166. Zbl0686.35111MR1012203
  4. [4] Christodoulou D., Lindblad H., On the motion of the free surface of a liquid, Comm. Pure Appl. Math.53 (12) (2000) 1536-1602. Zbl1031.35116MR1780703
  5. [5] Ebin D.G., The equations of motion of a perfect fluid with free boundary are not well posed, Comm. Partial Differential Equations12 (1987) 1175-1201. Zbl0631.76018MR886344
  6. [6] Evans L.C., Partial Differential Equations, Grad. Stud. Math., vol. 19, Amer. Math. Soc., 1998. Zbl0902.35002MR1625845
  7. [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. Zbl0897.76017MR1474190
  8. [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. Zbl0951.76011MR1690447
  9. [9] Kato T., Ponce G., Well-posedness of the Euler and Navier–Stokes equations in Lebesgue spaces, Rev. Mat. Iberoamericana2 (1986) 73-88. Zbl0615.35078MR864654
  10. [10] Lions J.L., Magenes E., Non-Homogeneous Boundary Value Problems and Applications, I, Grundlehren Math. Wiss., vol. 181, Springer-Verlag, 1972. Zbl0223.35039
  11. [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. Zbl1023.76007MR1946720
  12. [12] Okazawa N., The Euler equation on a bounded domain as a quasilinear evolution equation, Commun. Appl. Nonlinear Anal.3 (3) (1996) 107-113. Zbl0859.35100MR1397596
  13. [13] Renardy M., An existence theorem for a free surface flow problem with open boundaries, Comm. Partial Differential Equations17 (1992) 1387-1405. Zbl0767.35061MR1179291
  14. [14] Schweizer B., A two-component flow with a viscous and an inviscid fluid, Comm. Partial Differential Equations25 (2000) 887-901. Zbl0955.35062MR1759796
  15. [15] Triebel H., Theory of Function Spaces, Monographs Math., vol. 78, Birkhäuser, 1983. Zbl0546.46027MR781540
  16. [16] Triebel H., Theory of Function Spaces II, Monographs Math., vol. 84, Birkhäuser, 1992. Zbl0763.46025MR1163193
  17. [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. Zbl0930.35139MR1708476
  18. [18] Wu S., Well-posedness in Sobolev spaces of the full water wave problem in 2-D, Invent. Math.130 (1) (1997) 39-72. Zbl0892.76009MR1471885
  19. [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. Zbl0921.76017MR1641609

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