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

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 22, Issue 6, 2005, Pages 753-781

  Schweizer, Ben ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FLUID DYNAMICS; FUNCTIONS; LAGRANGE MULTIPLIERS; NAVIER STOKES EQUATIONS; PRESSURE MEASUREMENT; SURFACE TENSION; VISCOSITY; VORTEX FLOW;

COORDINATE SYSTEM; IDEAL FLUIDS; LAGRANGIAN COORDINATES; THREE-DIMENSIONAL EULER EQUATIONS;

BOUNDARY LAYER FLOW;

EID: 25644455336     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2004.11.001     Document Type: Article

References (19)

1. J.T. Beale Large time regularity of viscous surface waves Arch. Rat. Mech. Anal. 84 1984 307 352
2. K. Beyer, and M. Günther On the Cauchy problem for a capillary drop. I. Irrotational motion Math. Methods Appl. Sci. 21 12 1998 1149 1183
3. X. Chen, and A. Friedman A bubble in ideal fluid with gravity J. Differential Equations 81 1989 136 166
4. D. Christodoulou, and H. Lindblad On the motion of the free surface of a liquid Comm. Pure Appl. Math. 53 12 2000 1536 1602
5. D.G. Ebin The equations of motion of a perfect fluid with free boundary are not well posed Comm. Partial Differential Equations 12 1987 1175 1201
6. L.C. Evans Partial Differential Equations Grad. Stud. Math. vol. 19 1998 Amer. Math. Soc.
7. T. Iguchi, N. Tanaka, and A. Tani On the two-phase free boundary problem for two-dimensional water waves Math. Ann. 309 2 1997 199 223
8. T. Iguchi, N. Tanaka, and A. Tani On a free boundary problem for an incompressible ideal fluid in two space dimensions Adv. Math. Sci. Appl. 9 1 1999 415 472
9. T. Kato, and G. Ponce Well-posedness of the Euler and Navier-Stokes equations in Lebesgue spaces Rev. Mat. Iberoamericana 2 1986 73 88
10. J.L. Lions, and E. Magenes Non-Homogeneous Boundary Value Problems and Applications, I Grundlehren Math. Wiss. vol. 181 1972 Springer-Verlag
11. M. Ogawa, and A. Tani Free boundary problem for an incompressible ideal fluid with surface tension Math. Models Methods Appl. Sci. 12 12 2002 1725 1740
12. N. Okazawa The Euler equation on a bounded domain as a quasilinear evolution equation Commun. Appl. Nonlinear Anal. 3 3 1996 107 113
13. M. Renardy An existence theorem for a free surface flow problem with open boundaries Comm. Partial Differential Equations 17 1992 1387 1405
14. B. Schweizer A two-component flow with a viscous and an inviscid fluid Comm. Partial Differential Equations 25 2000 887 901
15. H. Triebel Theory of Function Spaces Monographs Math. vol. 78 1983 Birkhäuser
16. H. Triebel Theory of Function Spaces II Monographs Math. vol. 84 1992 Birkhäuser
17. A. Wagner On the Bernoulli free boundary problem with surface tension I. Athanasopoulos Free boundary problems: theory and applications CRC Res. Notes Math. vol. 409 1999 Chapman & Hall 246 251
18. S. Wu Well-posedness in Sobolev spaces of the full water wave problem in 2-D Invent. Math. 130 1 1997 39 72
19. S. Wu Well-posedness in Sobolev spaces of the full water wave problem in 3-D J. Amer. Math. Soc. 12 2 1999 445 495