On periodic Stokesian Hele-Shaw flows with surface tension

European Journal of Applied Mathematics

Volumn 19, Issue 6, 2008, Pages 717-734

  Escher, J ^a   Matioc, B V ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54049149365     PISSN: 09567925     EISSN: 14694425     Source Type: Journal    
DOI: 10.1017/S0956792508007699     Document Type: Article

References (14)

1. AMANN, H. (1995) Linear and Quasilinear Parabolic Problems, Vol. I, Birkhäuser, Basel, Switzerland.
2. ARENDT, W. & BU, S. (2004) Operator-valued Fourier multipliers on periodic Besov spaces and applications, Proceedings of the Edinburgh Mathematical Society 47, 15-33.
3. ESCHER, J. (1997) On moving boundaries in deformable media. Adv. Math. Sci. Appl. 7(1), 275-316.
4. ESCHER, J. & MATIOC, B.-V. (2008) A moving boundary problem for periodic Stokesian Hele-Shaw flows, Interfaces and Free Boundaries, to appear.
5. ESCHER, J. & MATIOC, B.-V. (2008) Stability of the equilibria for periodic Stokesian Hele-Shaw flows. J. Evol. Eq., online 8.7.2008.
6. ESCHER, J. & PROKERT, G. (2001) Stability of the equilibria for spatially periodic flows in porous media. Nonlin. Anal. 45, 1061-1080.
7. ESCHER, J. & SIMONETT, G. (1991) Maximal regularity for a free boundary problem. Nonlin. Diff. Eq. Appl. 2, 463-510.
8. ESCHER, J. & SIMONETT, G. (1996) Analyticity of the interface in a free boundary problem. Math. Ann. 305, 435-459.
9. ESCHER, J. & SIMONETT, G. (1997) Classical solutions of multidimensional Hele-Shaw models. SIAM J. Math. Anal. 28(5), 1028-1047.
10. GILBARG, D. & TRUDINGER, T. S. (1997) Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York.
11. KONDIC, L., PALFFY-MAHORNY, P. & SHELLEY, M. J. (1996) Models of non-Newtonian Hele-Shaw flow. Phys. Rev. E 54(5), R4536-R4539.
12. LUNARDI, A. (1995) Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel, Switzerland.
13. SCHMEISSER, H.-J. & TRIEBEL H. (1987) Topics in Fourier Analysis and Function Spaces, John Wiley and Sons, New York.
14. SHAUGHNESSY, E. J., KATZ, I. M. & SCHAFFER, J. P. (2005) Introduction to Fluid Mechanics, Oxford University Press, New York.