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].
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}, volume = {33}, number = {6}, year = {2016}, doi = {10.1016/j.anihpc.2015.05.006}, zbl = {1360.35175}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.006/} }
TY - JOUR AU - Eleuteri, Michela AU - Rocca, Elisabetta AU - Schimperna, Giulio TI - Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1431 EP - 1454 VL - 33 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.006/ DO - 10.1016/j.anihpc.2015.05.006 LA - en ID - AIHPC_2016__33_6_1431_0 ER -
%0 Journal Article %A Eleuteri, Michela %A Rocca, Elisabetta %A Schimperna, Giulio %T Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1431-1454 %V 33 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.006/ %R 10.1016/j.anihpc.2015.05.006 %G en %F AIHPC_2016__33_6_1431_0
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, Volume 33 (2016) no. 6, pp. 1431-1454. doi : 10.1016/j.anihpc.2015.05.006. http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.006/
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