Geodesic
Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1431-1454

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We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. The model was recently introduced in [11] where existence of weak solutions was proved in three space dimensions. Here, we aim to study the properties of solutions in the two-dimensional case. In particular, we can show existence of global in time solutions satisfying a stronger formulation of the model with respect to the one considered in [11].

DOI : 10.1016/j.anihpc.2015.05.006
Classification : 35Q35, 35K25, 76D05, 35D30
Keywords: Cahn–Hilliard, Navier–Stokes, Incompressible non-isothermal binary fluid, Global-in-time existence, A-priori estimates 
@article{AIHPC_2016__33_6_1431_0,
     author = {Eleuteri, Michela and Rocca, Elisabetta and Schimperna, Giulio},
     title = {Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1431--1454},
     publisher = {Elsevier},
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     number = {6},
     year = {2016},
     doi = {10.1016/j.anihpc.2015.05.006},
     zbl = {1360.35175},
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Eleuteri, Michela; Rocca, Elisabetta; Schimperna, Giulio. Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1431-1454. doi: 10.1016/j.anihpc.2015.05.006

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