@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://www.numdam.org/item/AIHPC_2001__18_2_225_0/} }
Boyer, Franck. Nonhomogeneous Cahn-Hilliard fluids. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 2, pp. 225-259. http://www.numdam.org/item/AIHPC_2001__18_2_225_0/
[1] Sobolev Spaces, Pure and Applied Mathematics, 65, Academic Press, New York, 1975. | MR | Zbl
,[2] Slow motion for the Cahn-Hilliard equation in one space dimension, J. Differential Equation 90 (1991) 81-135. | Zbl
, , ,[3] Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, 2, 1965. | MR | Zbl
,[4] The dynamics of nucleation for the Cahn-Hilliard equation, SIAM J. Appl. Math. 53 (4) (1993) 990-1008. | Zbl
, ,[5] Mathematical study of multiphase flow under shear through order parameter formulation, Asymptotic Analysis 20 (2) (1999) 175-212. | MR | Zbl
,[6] 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] Structured phase transitions on a finite interval, Arch. Rational Mech. Anal. 86 (1984) 317-351. | MR | Zbl
, , ,[9] Mixing of a two-phase fluid by a cavity flow, Physical Review E 53 (1996) 3832.
, ,[10] On the Cahn-Hilliard equation with a logarithmic free energy, Nonlinear Analysis 24 (10) (1995) 1491-1514. | Zbl
, ,[11] Dynamics of domains and textures, in: Theoretical Challenges in the Dynamics of Complex Fluids, 1997, pp. 293-314.
,[12] On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal. 27 (2) (1996) 404-423. | Zbl
, ,[13] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1977. | MR | Zbl
, ,[14] Phase Transitions and Critical Phenomena, Vol. 8, Academic, London, 1983. | MR
, , , , (Eds.),[15] 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] Korn's inequalities and their applications in continuum mechanics, SIAM Review 37 (4) (1995) 491-511. | MR | Zbl
,[17] Coarse-grained description of thermo-capillary flow, Phys. Fluids 8 (1996) 660. | Zbl
, ,[18] Problèmes aux Limites non Homogènes et Applications, Dunod, 1968. | Zbl
, ,[19] Mathematical Topics in Fluid Mechanics: Vol. 1, Incompressible Models, Oxford Science Publications, 1996. | MR | Zbl
,[20] 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] 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] Some global dynamical properties of a class of pattern formation equations, Comm. Partial Differential Equations 14 (2) (1989) 245-297. | MR | Zbl
, , ,[23] Phase transitions of fluids in shear flow, J. Phys.: Condens. Matter 9 (1997) 6119-6157.
,[24] Compact sets in the space Lp(0,T;B), Ann. Mat. Pura Appl. 146 (4) (1987) 65-96. | MR | Zbl
,[25] Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Science, 68, Springer-Verlag, 1997. | MR | Zbl
,[26] Navier-Stokes Equations, Studies in Mathematics and its Applications, 2, North-Holland, Amsterdam, 1977. | Zbl
,[27] Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. Henri Poincaré: Analyse non linéaire 15 (4) (1998) 459-492. | Numdam | Zbl
, ,[28] On the stationary Cahn-Hilliard equation: interior spike solutions, J. Differential Equations 148 (2) (1998) 231-267. | Zbl
, ,[29] On the stationary Cahn-Hilliard equation: bubble solutions, SIAM J. Math. Anal. 29 (6) (1998) 1492-1518. | Zbl
, ,