Well-posedness of the Hele–Shaw–Cahn–Hilliard system
Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 367-384.

We study the well-posedness of the Hele–Shaw–Cahn–Hilliard system modeling binary fluid flow in porous media with arbitrary viscosity contrast but matched density between the components. For initial data in H s , s>d 2+1, the existence and uniqueness of solution in C([0,T];H s )∩L 2 (0,T;H s+2 ) that is global in time in the two dimensional case (d=2) and local in time in the three dimensional case (d=3) are established. Several blow-up criterions in the three dimensional case are provided as well. One of the tools that we utilized is the Littlewood–Paley theory in order to establish certain key commutator estimates.

DOI : 10.1016/j.anihpc.2012.06.003
Mots-clés : Hele–Shaw–Cahn–Hilliard, Well-posedness, Blow-up criterion 
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     title = {Well-posedness of the {Hele{\textendash}Shaw{\textendash}Cahn{\textendash}Hilliard} system},
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Wang, Xiaoming; Zhang, Zhifei. Well-posedness of the Hele–Shaw–Cahn–Hilliard system. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 3, pp. 367-384. doi : 10.1016/j.anihpc.2012.06.003. http://www.numdam.org/articles/10.1016/j.anihpc.2012.06.003/

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