Nonhomogeneous Cahn-Hilliard fluids
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 2, pp. 225-259. 
@article{AIHPC_2001__18_2_225_0,
     author = {Boyer, Franck},
     title = {Nonhomogeneous {Cahn-Hilliard} fluids},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {225--259},
     publisher = {Elsevier},
     volume = {18},
     number = {2},
     year = {2001},
     zbl = {1037.76062},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2001__18_2_225_0/}
}
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Boyer, Franck. Nonhomogeneous Cahn-Hilliard fluids. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 2, pp. 225-259. http://archive.numdam.org/item/AIHPC_2001__18_2_225_0/

[1] Adams R.A., Sobolev Spaces, Pure and Applied Mathematics, 65, Academic Press, New York, 1975. | MR | Zbl

[2] Alikakos N., Bates P., Fusco G., Slow motion for the Cahn-Hilliard equation in one space dimension, J. Differential Equation 90 (1991) 81-135. | Zbl

[3] Agmon S., Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, 2, 1965. | MR | Zbl

[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. | Zbl

[5] Boyer F., Mathematical study of multiphase flow under shear through order parameter formulation, Asymptotic Analysis 20 (2) (1999) 175-212. | MR | Zbl

[6] Boyer F., A theoretical and numerical model for the study of incompressible mixture flows, Computers and Fluids (2000), to appear. | MR | Zbl

[7] Colin A., Panizza P., Private communications.

[8] Carr J., Gurtin M., Slemrod M., Structured phase transitions on a finite interval, Arch. Rational Mech. Anal. 86 (1984) 317-351. | MR | Zbl

[9] Chella R., Vinals J., Mixing of a two-phase fluid by a cavity flow, Physical Review E 53 (1996) 3832.

[10] Debussche A., Dettori L., On the Cahn-Hilliard equation with a logarithmic free energy, Nonlinear Analysis 24 (10) (1995) 1491-1514. | Zbl

[11] Doi M., Dynamics of domains and textures, in: Theoretical Challenges in the Dynamics of Complex Fluids, 1997, pp. 293-314.

[12] Elliott C.M., Garcke H., On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. 27 (2) (1996) 404-423. | Zbl

[13] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977. | MR | Zbl

[14] Gunton J.D., San Miguel M., Sahni P.S., Domb , Lebowitz (Eds.), Phase Transitions and Critical Phenomena, Vol. 8, Academic, London, 1983. | MR

[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 Sciences 6 (1996) 815. | MR | Zbl

[16] Horgan C.O., Korn's inequalities and their applications in continuum mechanics, SIAM Review 37 (4) (1995) 491-511. | MR | Zbl

[17] Jasnow D., Vinals J., Coarse-grained description of thermo-capillary flow, Phys. Fluids 8 (1996) 660. | Zbl

[18] Lions J.L., Magenes E., Problèmes aux Limites non Homogènes et Applications, Dunod, 1968. | Zbl

[19] Lions P.L., Mathematical Topics in Fluid Mechanics: Vol. 1, Incompressible Models, Oxford Science Publications, 1996. | MR | Zbl

[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. | MR

[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. | Zbl

[22] Nicolaenko B., Scheurer B., Temam R., Some global dynamical properties of a class of pattern formation equations, Comm. Partial Differential Equations 14 (2) (1989) 245-297. | MR | Zbl

[23] Onuki A., Phase transitions of fluids in shear flow, J. Phys.: Condens. Matter 9 (1997) 6119-6157.

[24] Simon J., Compact sets in the space Lp(0,T;B), Ann. Mat. Pura Appl. 146 (4) (1987) 65-96. | MR | Zbl

[25] Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Science, 68, Springer-Verlag, 1997. | MR | Zbl

[26] Temam R., Navier-Stokes Equations, Studies in Mathematics and its Applications, 2, North-Holland, Amsterdam, 1977. | Zbl

[27] Wei J., Winter M., Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. Henri Poincaré: Analyse non linéaire 15 (4) (1998) 459-492. | Numdam | Zbl

[28] Wei J., Winter M., On the stationary Cahn-Hilliard equation: interior spike solutions, J. Differential Equations 148 (2) (1998) 231-267. | Zbl

[29] Wei J., Winter M., On the stationary Cahn-Hilliard equation: bubble solutions, SIAM J. Math. Anal. 29 (6) (1998) 1492-1518. | Zbl