Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids

Eleuteri, Michela; Rocca, Elisabetta; Schimperna, Giulio

Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1431-1454.

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].

Classification : 35Q35, 35K25, 76D05, 35D30
Mots clés : Cahn–Hilliard, Navier–Stokes, Incompressible non-isothermal binary fluid, Global-in-time existence, A-priori estimates

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