On a Diffuse Interface Model for Two-Phase Flows of Viscous, Incompressible Fluids with Matched Densities, Archive for Rational Mechanics and Analysis, vol.141, issue.4, pp.463-506, 2009. ,
DOI : 10.1007/s002050050081
Sobolev spaces, 2003. ,
DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS, Annual Review of Fluid Mechanics, vol.30, issue.1, pp.139-165, 1998. ,
DOI : 10.1146/annurev.fluid.30.1.139
URL : http://hdl.handle.net/2060/19980000187
Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, 1973. ,
Functional Analysis, Sobolev Spaces and partial Differential Equations, 2010. ,
DOI : 10.1007/978-0-387-70914-7
On the Cahn???Hilliard???Brinkman system, Communications in Mathematical Sciences, vol.13, issue.6, pp.1541-1567, 2015. ,
DOI : 10.4310/CMS.2015.v13.n6.a9
Mathematical study of multi-phase flow under shear through order parameter formulation, Asymptot . Anal, vol.20, pp.175-212, 1999. ,
Nonhomogeneous Cahn???Hilliard fluids, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.18, issue.2, pp.225-259, 2001. ,
DOI : 10.1016/S0294-1449(00)00063-9
URL : https://hal.archives-ouvertes.fr/hal-00004085
Mathematical tools for the study of the incompressible Navier-Stokes equations and related models ,
DOI : 10.1007/978-1-4614-5975-0
URL : https://hal.archives-ouvertes.fr/hal-00777731
A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow, Turbulence and Combustion, vol.15, issue.1, pp.1-27, 1947. ,
DOI : 10.1002/andp.19063240204
Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics, vol.184, issue.2, pp.258-267, 1958. ,
DOI : 10.1039/df9531500210
Mixing of a two-phase fluid by cavity flow, Physical Review E, vol.24, issue.4, pp.3832-3840, 1996. ,
DOI : 10.1021/i100018a006
Diffuse-interface approach to rotating Hele-Shaw flows, Physical Review E, vol.5, issue.4, p.46302, 2011. ,
DOI : 10.1016/j.jcp.2009.09.039
Abstract, Communications in Computational Physics, vol.7, issue.04, pp.929-957, 2013. ,
DOI : 10.1016/S0167-2789(03)00030-7
The nonlocal Cahn???Hilliard equation with singular potential: Well-posedness, regularity and strict separation property, Journal of Differential Equations, vol.263, issue.9, pp.5253-5297, 2017. ,
DOI : 10.1016/j.jde.2017.06.015
Asymptotic behavior of a Cahn???Hilliard???Navier???Stokes system in 2D, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.27, issue.1, pp.401-436, 2010. ,
DOI : 10.1016/j.anihpc.2009.11.013
Cahn???Hilliard???Navier???Stokes systems with moving contact lines, Calculus of Variations and Partial Differential Equations, vol.14, issue.3, pp.50-51, 2016. ,
DOI : 10.1016/j.nonrwa.2012.09.003
URL : https://hal.archives-ouvertes.fr/hal-01135747
Global weak solutions and asymptotic limits of a Cahn???Hilliard???Darcy system modelling tumour growth, AIMS Mathematics, vol.1, issue.3, pp.318-360, 2016. ,
DOI : 10.3934/Math.2016.3.318
A Cahn???Hilliard???Darcy model for tumour growth with chemotaxis and active transport, Mathematical Models and Methods in Applied Sciences, vol.42, issue.06, pp.1095-1148, 2016. ,
DOI : 10.1016/j.jtbi.2008.03.027
URL : http://arxiv.org/pdf/1509.03655
The Cahn-Hilliard-Hele-Shaw with singular potential, Ann. Inst. H. Poincaré Anal. Non Linéaire ,
URL : https://hal.archives-ouvertes.fr/hal-01543386
The Cahn???Hilliard???Oono equation with singular potential, Mathematical Models and Methods in Applied Sciences, vol.40, issue.13, pp.2485-2510, 2017. ,
DOI : 10.1016/S0362-546X(99)00402-2
TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER, Mathematical Models and Methods in Applied Sciences, vol.06, issue.06, pp.815-831, 1996. ,
DOI : 10.1142/S0218202596000341
Effects of Reversible Chemical Reaction on Morphology and Domain Growth of Phase Separating Binary Mixtures with Viscosity Difference, Macromolecular Theory and Simulations, vol.13, issue.3, pp.280-289, 2004. ,
DOI : 10.1002/mats.200300021
Abstract, Communications in Computational Physics, vol.7, issue.03, pp.613-661, 2012. ,
DOI : 10.1016/S0167-2789(03)00030-7
URL : https://hal.archives-ouvertes.fr/hal-01058407
Modeling pinchoff and reconnection in a Hele-Shaw cell. I. The models and their calibration, Physics of Fluids, vol.174, issue.2, pp.492-513, 2002. ,
DOI : 10.1016/S0022-0248(96)01060-3
Finite-dimensional global attractor of the Cahn???Hilliard???Brinkman system, Journal of Mathematical Analysis and Applications, vol.434, issue.1, pp.599-616, 2016. ,
DOI : 10.1016/j.jmaa.2015.09.026
A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier spectral method, Phys, pp.211-228, 2003. ,
Nonlinear modelling of cancer: bridging the gap between cells and tumours, Nonlinearity, vol.23, issue.1, pp.1-91, 2010. ,
DOI : 10.1088/0951-7715/23/1/R01
Analysis of a mixture model of tumor growth, European Journal of Applied Mathematics, vol.23, issue.05, pp.691-734, 2013. ,
DOI : 10.1016/0022-0396(91)90163-4
On the Cahn-Hilliard-Oono-Navier-Stokes equations with singular potentials, Applicable Analysis, vol.7, issue.12, pp.95-2609, 2016. ,
DOI : 10.1137/S0036141094267662
Robust exponential attractors for Cahn-Hilliard type equations with singular potentials, Mathematical Methods in the Applied Sciences, vol.27, issue.5, pp.545-582, 2004. ,
DOI : 10.1002/mma.464
Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcial. Ekvac, vol.40, pp.411-433, 1997. ,
Theoretical studies of phase-separation kinetics in a Brinkman porous medium, Journal of Physics A: Mathematical and Theoretical, vol.43, issue.20, 2010. ,
DOI : 10.1088/1751-8113/43/20/202001
Universal attractor for some singular phase transition systems, Physica D: Nonlinear Phenomena, vol.192, issue.3-4, pp.279-307, 2004. ,
DOI : 10.1016/j.physd.2004.01.024
URL : http://www.mat.unimi.it/users/rocca/correctrs.pdf
Derivation of effective macroscopic Stokes???Cahn???Hilliard equations for periodic immiscible flows in porous media, Nonlinearity, vol.26, issue.12, pp.3259-3277, 2013. ,
DOI : 10.1088/0951-7715/26/12/3259
Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval, Annali di Matematica Pura ed Applicata, vol.146, issue.1, pp.117-148, 1990. ,
DOI : 10.1007/BF02684796
Infinite-dimensional dynamical systems in mechanics and physics, Second Edition, Applied Mathematical Sciences, vol.68, 1997. ,
DOI : 10.1007/978-1-4684-0313-8
Diffuse-interface modeling of thermocapillary flow instabilities in a Hele-Shaw cell, J. Fluid Mech, vol.434, pp.153-166, 2001. ,
Long-time behavior for the Hele-Shaw-Cahn-Hilliard system, Asymptot. Anal, vol.78, pp.217-245, 2012. ,
Well-posedness of the Hele???Shaw???Cahn???Hilliard system, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.30, issue.3, pp.367-384, 2013. ,
DOI : 10.1016/j.anihpc.2012.06.003
Convergence to equilibrium for a phase-field model for the mixture of two incompressible fluids, Commun. Math. Sci, vol.7, pp.939-962, 2009. ,
Well-posedness and global attractor of the Cahn-Hilliard-Brinkman system with dynamic boundary conditions, Dyn. Partial Differ, Eqns, vol.13, pp.75-90, 2016. ,
ITALY E-mail address: monica.conti@polimi, p.27100, 20133. ,