Dynamics near unstable, interfacial fluids

Communications in Mathematical Physics

Volumn 270, Issue 3, 2007, Pages 635-689

  Guo, Yan ^a   Hallstrom, Chris ^b   Spirn, Daniel ^c  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF PORTLAND   (United States)

^c UNIVERSITY OF MINNESOTA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846818718     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0164-4     Document Type: Article

References (31)

1. Almeida, L., Bethuel, F., Guo, Y.: A remark on the instability of symmetric vortices with large coupling constant. Comm. Pure Appl. Math. 50, 1295-1300 (1997)
2. Ambrose, D.: Well-Posedness of Vortex Sheets with Surface Tension. SIAM J. Math. Anal. 35, 221244 (2003)
3. Ambrose, D.: Well-posedness of two-phase Hele-Shaw flow without surface tension. Euro. J. Appl. Math. 15, 597-607 (2004)
4. Bardos, C., Guo, Y., Strauss, W.: Stable and unstable ideal plane flows. Dedicated to the memory of Jacques-Louis Lions. Chinese Ann. Math. Ser. B 23, 149-164 (2002)
5. Baker, G., Meiron, D., Orszag, S.: Generalized vortex methods for free-surface flow problems. J. Fluid Mech. 123, 477-501 (1982)
6. Beale, J.T., Hou, T., Lowengrub, .T.: Growth rates for the linearized motion of fluid interfaces away from equilibrium. Comm. Pure Appl. Math. 46, 1269-1301 (1993)
7. Bertozzi, A., Constantin, P.: Global regularity for vortex patches. Commun. Math. Phys. 152, 1928 (1993)
8. Chemin, J.-Y.: Persistance de structures geometriques dans les fluides incompressibles bidimensionals. Ann. EC. Norm. Super. 26, 1-16 (1993)
9. Constantin, P., Titi, E. : On the evolution of nearly circular vortex patches. Commun. Math. Phys. 119, 177198 (1988)
10. Cordier, S., Grenier, E., Guo, Y.: Two-stream instabilities in plasmas. Cathleen Morawetz: a great mathematician. Methods Appl. Anal. 7, 391-405 (2000)
11. Escher, J., Simonett, G.: Classical solutions for Hele-Shaw models with surface tension. Adv. Differ. Eqs. 2, 619-642 (1997)
12. Friedlander, S., Strauss, W., Vishik, M.: Nonlinear instability in an ideal fluid. Ann. Inst. H. Poincaré Anal. Non Linéaire 14, 187-209 (1997)
13. Grenier, E.: On the nonlinear instability of Euler and Prandtl equations. Comm. Pure Appl. Math. 53, 1067-1091 (2000)
14. Guo, Y., Hallstrom, C., Spirn, D.: Dynamics near an unstable Kirchhoff ellipse. Commun. Math. Phys. 245, 297-354 (2004)
15. Guo, Y., Strauss, W.: Instability of periodic BGK equilibria. Comm. Pure Appl. Math. 48, 861-894 (1995)
16. Hou, T., Lowengrub, J., Shelley, M.: Removing the stiffness from interfacial flows with surface tension. J. Comp. Phys. 114, 312-338 (1994)
17. Hou, T., Lowengrub, J., Shelley, M.: The long-time motion of vortex sheets with surface tension. Phys. Fluids 9, 1933-1954 (1997)
18. Hwang, H.J., Guo, Y: On the dynamical Rayleigh-Taylor instability. Arch. Rat. Mech. Anal. 167, 235253 (2003)
19. Iguchi, T.: Well-posedness of the initial value problem for capillary-gravity waves. Funkcial. Ekvac. 44, 219-241 (2001)
20. Lin, Z. : Nonlinear instability of ideal plane flows. Inter. Math. Res. Not. 41, 2147-2178 (2004)
21. Love, A.E.: On the stability of certain vortex motion. Proc. Soc. Lond. 23, 18-42 (1893)
22. Majda, A., Bertozzi, A.: Vorticity and incompressible flow. Cambridge Texts in Applied Mathematics 27. Cambridge: Cambridge University Press (2002)
23. Ogawa, M., Tani, A.: Free boundary problem for an incompressible ideal fluid with surface tension. Math. Models Methods Appl. Sci. 12, 1725-1740 (2002)
24. Saffman, P.: Vortex dynamics. Cambridge Monographs on Mechanics and Applied Mathematics. New York: Cambridge University Press (1992)
25. Siegal, M., Caflisch, R., Howison, S.: Global existence, singular solutions, and ill-posedness for the Muskat problem. Comm. Pure Appl. Math. 57, 1374-1411 (2004)
26. Tang, Y.: Nonlinear stability of vortex patches. Trans. AMS, 304, 617-638 (1987)
27. Taylor, M.:Tools for PDE. In: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials. Providence, RI: Amer. Math. Soc., (1991)
28. Vishik, M., Friedlander, S.: Nonlinear instability in two dimensional ideal fluids: the case of a dominant eigenvalue. Commun. Math. Phys. 243, 261-273 (2003)
29. Wan, Y.H.: The stability of rotating voitex patches. Commun. Math. Phys. 107, 1-20 (1986)
30. Wan, Y.H., Pulvirenti, M.: Nonlinear stability of circular vortex patches. Commun. Math. Phys. 99, 435450 (1985)
31. Wu, S.: Mathematical analysis of voitex sheets. Comm. Pure Appl. Math. 59, 1065-1206 (2006)