Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse

Physics of Fluids

Volumn 11, Issue 10, 1999, Pages 2809-2811

  Pesci, Adriana J ^a   Goldstein, Raymond E ^a   Shelley, Michael J ^b  

^a UNIVERSITY OF ARIZONA   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000107553     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.870139     Document Type: Article

References (14)

1. G. Tryggvason and H. Aref, "Numerical experiments on Hele-Shaw flow with a sharp interface," J. Fluid Mech. 136, 1 (1983).
2. S. Cardoso and A. Wood, "The formation of drops through viscous instability," J. Fluid Mech. 289, 351 (1995).
3. R. E. Goldstein, A. I. Pesci, and M. J. Shelley, "Topology transitions and singularities in viscous flows," Phys. Rev. Lett. 70, 3043 (1993).
4. R. E. Goldstein, A. I. Pesci, and M. J. Shelley, "Attracting manifold for a viscous topology transition," Phys. Rev. Lett. 75, 3665 (1995); "Instabilities and singularities in Hele-Shaw flow," Phys. Fluids 10, 2701 (1998).
5. R. E. Goldstein, A. I. Pesci, and M. J. Shelley, "Attracting manifold for a viscous topology transition," Phys. Rev. Lett. 75, 3665 (1995); "Instabilities and singularities in Hele-Shaw flow," Phys. Fluids 10, 2701 (1998).
6. P. Constantin, T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, M. Shelley, and S.-M. Zhou, "Droplet breakup in a model of the Hele-Shaw cell," Phys. Rev. E 47, 4169 (1993); T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, and S.-M. Zhou, "Finite-time singularity formation in Hele-Shaw systems," ibid. 47, 4182 (1993).
7. P. Constantin, T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, M. Shelley, and S.-M. Zhou, "Droplet breakup in a model of the Hele-Shaw cell," Phys. Rev. E 47, 4169 (1993); T. F. Dupont, R. E. Goldstein, L. P. Kadanoff, and S.-M. Zhou, "Finite-time singularity formation in Hele-Shaw systems," ibid. 47, 4182 (1993).
8. A. L. Bertozzi, "Symmetric singularity formation in lubrication-type equations for interface motion," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 681 (1996); A. L. Bertozzi, M. P. Brenner, T. F. Dupont, and L. P. Kadanoff, in Centennial Edition, Applied Mathematics Series, edited by L. Sirovich (Springer-Verlag, New York, 1993).
9. A. L. Bertozzi, "Symmetric singularity formation in lubrication-type equations for interface motion," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 56, 681 (1996); A. L. Bertozzi, M. P. Brenner, T. F. Dupont, and L. P. Kadanoff, in Centennial Edition, Applied Mathematics Series, edited by L. Sirovich (Springer-Verlag, New York, 1993).
10. R. Almgren, A. Bertozzi, and M. Brenner, "Stable and unstable singularities in the unforced Hele-Shaw cell," Phys. Fluids A 8, 1356 (1996).
11. A. Bertozzi and M. Pugh, "The lubrication approximation for thin viscous films: Regularity and long time behavior of weak solutions," Commun. Pure Appl. Math. 49, 85 (1996); "Long-wave instabilities and saturation in thin film equations," ibid. 51, 625 (1998).
12. A. Bertozzi and M. Pugh, "The lubrication approximation for thin viscous films: Regularity and long time behavior of weak solutions," Commun. Pure Appl. Math. 49, 85 (1996); "Long-wave instabilities and saturation in thin film equations," ibid. 51, 625 (1998).
13. J. Eggers, "Nonlinear dynamics and breakup of free-surface flows," Rev. Mod. Phys. 69, 865 (1997).
14. This analysis is in the same spirit as Moore's study of vortex sheet singularities; D. W. Moore, "The spontaneous appearance of a singularity in the shape of an evolving vortex sheet," Proc. R. Soc. London, Ser. A 365, 105 (1979).