Nonhomogeneous Cahn–Hilliard fluids

 Access to full text

 Full (PDF)

1. [1] Adams R.A., Sobolev Spaces, Pure and Applied Mathematics, 65, Academic Press, New York, 1975. Zbl0314.46030MR450957
2. [2] Alikakos N., Bates P., Fusco G., Slow motion for the Cahn–Hilliard equation in one space dimension, J. Differential Equation90 (1991) 81-135. Zbl0753.35042
3. [3] Agmon S., Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, 2, 1965. Zbl0142.37401MR178246
4. [4] Bates P.W., Fife P.C., The dynamics of nucleation for the Cahn–Hilliard equation, SIAM J. Appl. Math.53 (4) (1993) 990-1008. Zbl0788.35061
5. [5] Boyer F., Mathematical study of multiphase flow under shear through order parameter formulation, Asymptotic Analysis20 (2) (1999) 175-212. Zbl0937.35123MR1700669
6. [6] Boyer F., A theoretical and numerical model for the study of incompressible mixture flows, Computers and Fluids (2000), to appear. Zbl1057.76060MR1870172
7. [7] Colin A., Panizza P., Private communications. 
8. [8] Carr J., Gurtin M., Slemrod M., Structured phase transitions on a finite interval, Arch. Rational Mech. Anal.86 (1984) 317-351. Zbl0564.76075MR759767
9. [9] Chella R., Vinals J., Mixing of a two-phase fluid by a cavity flow, Physical Review E53 (1996) 3832. 
10. [10] Debussche A., Dettori L., On the Cahn–Hilliard equation with a logarithmic free energy, Nonlinear Analysis24 (10) (1995) 1491-1514. Zbl0831.35088
11. [11] Doi M., Dynamics of domains and textures, in: Theoretical Challenges in the Dynamics of Complex Fluids, 1997, pp. 293-314. 
12. [12] Elliott C.M., Garcke H., On the Cahn–Hilliard equation with degenerate mobility, SIAM J. Math. Anal.27 (2) (1996) 404-423. Zbl0856.35071
13. [13] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977. Zbl0361.35003MR473443
14. [14] Gunton J.D., San Miguel M., Sahni P.S., Domb, Lebowitz (Eds.), Phase Transitions and Critical Phenomena, Vol. 8, Academic, London, 1983. MR794319
15. [15] Gurtin M.E., Polignone D., Vinals J., Two-phase binary fluids and immiscible fluids described by an order parameter, Mathematical Models and Methods in Applied Sciences6 (1996) 815. Zbl0857.76008MR1404829
16. [16] Horgan C.O., Korn's inequalities and their applications in continuum mechanics, SIAM Review37 (4) (1995) 491-511. Zbl0840.73010MR1368384
17. [17] Jasnow D., Vinals J., Coarse-grained description of thermo-capillary flow, Phys. Fluids8 (1996) 660. Zbl1025.76521
18. [18] Lions J.L., Magenes E., Problèmes aux Limites non Homogènes et Applications, Dunod, 1968. Zbl0165.10801
19. [19] Lions P.L., Mathematical Topics in Fluid Mechanics: Vol. 1, Incompressible Models, Oxford Science Publications, 1996. Zbl0866.76002MR1422251
20. [20] Miranville A., Upper bound on the dimension of the attractor for the shear-layer flow in space dimension 3, in: Dynamical Systems, Stockholm, 1992, World Sci. Publishing, River Edge, NJ, 1993, pp. 61-74. MR1386915
21. [21] Miranville A., A model of Cahn–Hilliard equation based on a microforce balance, C. R. Acad. Sci. Paris Sér. I Math.328 (12) (1999) 1247-1252. Zbl0932.35118
22. [22] Nicolaenko B., Scheurer B., Temam R., Some global dynamical properties of a class of pattern formation equations, Comm. Partial Differential Equations14 (2) (1989) 245-297. Zbl0691.35019MR976973
23. [23] Onuki A., Phase transitions of fluids in shear flow, J. Phys.: Condens. Matter9 (1997) 6119-6157. 
24. [24] Simon J., Compact sets in the space Lp(0,T;B), Ann. Mat. Pura Appl.146 (4) (1987) 65-96. Zbl0629.46031MR916688
25. [25] Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Science, 68, Springer-Verlag, 1997. Zbl0871.35001MR1441312
26. [26] Temam R., Navier–Stokes Equations, Studies in Mathematics and its Applications, 2, North-Holland, Amsterdam, 1977. Zbl0383.35057
27. [27] Wei J., Winter M., Stationary solutions for the Cahn–Hilliard equation, Ann. Inst. Henri Poincaré: Analyse non linéaire15 (4) (1998) 459-492. Zbl0910.35049
28. [28] Wei J., Winter M., On the stationary Cahn–Hilliard equation: interior spike solutions, J. Differential Equations148 (2) (1998) 231-267. Zbl0965.35070
29. [29] Wei J., Winter M., On the stationary Cahn–Hilliard equation: bubble solutions, SIAM J. Math. Anal.29 (6) (1998) 1492-1518. Zbl0918.35023