Existence results for the quasistationary motion of a free capillary liquid drop

Zeitschrift für Analysis und ihre Anwendungen

Volumn 16, Issue 2, 1997, Pages 311-348

  Gunther M ^a  

^a UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744445483     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/765     Document Type: Article

References (22)

1. Abergel, F.:A geometric approach to the study of stationary free surface flows for viscous liquids. Proc. Royal Soc. Edinburgh 123A (1993), 209 - 229.
2. Abergel, F. and E. Rouy:Interfaces stationnaires pour les équations de Navier-Stokes. Inst. Nat. Rech. Inf. Aut. (INRIA) Research Report No. 2651 (1995), pp. 45.
3. Antanovskii, L. K.:Analyticity of a free boundary in plane quasi-steady flow of a liquid form subject to variable surface tension. Lect. Notes Math. 1530 (1993), 1 - 16.
4. Antanovskii, L. K.:Creeping thermocapillary motion of a two-dimensional deformable bubble: existence theorem and numerical simulation. Eur. J. Mech./Issue B: Fluids 11 (1992), 741 - 758.
5. Blaschke, W. and K. Leichtweiß:Elementare Differentialgeometrie. Berlin et al.: SpringerVerlag 1973.
6. Brezzi, F. and M. Fortin:Mixed and Hybrid Finite Element methods. Berlin et al.: Springer-Verlag 1991.
7. Chen, X.:The Hele-Shaw problem and area-preserving curve-shortening motions. Arch. Rat. Mech. Anal. 123 (1993), 117 - 151.
8. Constantin, P. and L. Kadanoff:Dynamics of a complex interface. Physica 47D (1991), 450 - 460.
9. Constantin, P. and M. Pugh:Global solution for small data to the Hele-Shaw problem. Nonlinearity 6 (1993), 393 - 415.
10. Courant, R. and D. Hilbert:Methoden der mathematischen Physik. Vol. 2. Berlin et al.; Springer-Verlag 1968.
11. Fichera, G.:Existence theorems in elasticity. In: Handbuch der Physik, Vol. VIa/II (ed.: S. Flügge). Berlin et al.: Springer-Verlag 1972.
12. Galdi, G. P.:An Introduction to the Mathematical Theory of Navier-Stokes-Equations, Vol. I (Springer Tracts in Natural Philosophy: Vol. 38). New York et. al.: SpringerVerlag 1994.
13. Günther, M. and G. Prokert:Existence results for the quasistationary motion of a viscous capillary liquid drop. Preprint. Eindhoven: Univ. of Technology, Preprint RANA 96-01 (1996), pp. 55.
14. Hopper, R. W.:Plane Stokes flow driven by capillarity on a free surface. J. Fluid Mech. 213 (1990), 349 - 375.
15. Kato, T. and C. Y. Lai:Nonlinear evolution equations and the Euler flow. J. Funct. Anal. 56 (1984), 15 - 28.
16. Klein Obbink:Moving Boundary Problems in Relation with Equations of Löwner-Kufarev Type. PhD Thesis. Eindhoven: University of Technology 1995.
17. Ladyshenskaja, O. A.:Funktionalanalytische Untersuchungen der Navier-Stokes-Gleichungen. Berlin: Dt. Verlag Wiss. 1965.
18. Prokert, G.:On the existence of solutions in plane quasistationary Stokes flow driven by surface tension. Euro. J. Appl. Math. 6 (1995), 539 - 558.
19. Seeley, R.:Topics in pseudo-differential operators. In: Pseudo-differential Operators (ed.: L. Nirenberg). Centro Intern. Mat. Estivo (C.I.M.E.) Proceedings, Rome 1969, pp. 169 -305.
20. Triebel, H.:Höhere Analysis. Berlin: Dt. Verlag Wiss. 1972.
21. Vorst, G. A. L. v. d.:Modelling and Numerical Simulation of Viscous Sintering. PhD Thesis. Eindhoven: University of Technology 1994.
22. Zeidler, E.:Vorlesungen über nichtlineare Funktionalanalysis. Vol. I: Fixpunktsätze. Leipzig: B. G. Teubner Verlagsges. 1976.