JournalsaihpcVol. 33, No. 6pp. 1431–1454

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

  • Michela Eleuteri

    Dipartimento di Matematica ed Informatica “U. Dini”, viale Morgagni 67/a, I-50134 Firenze, Italy

  • Elisabetta Rocca

    Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany, Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, I-20133 Milano, Italy

  • Giulio Schimperna

    Dipartimento di Matematica “F. Casorati”, Università degli Studi di Pavia, via Ferrata 1, I-27100 Pavia, Italy
Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids cover
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Abstract

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].

Cite this article

Michela Eleuteri, Elisabetta Rocca, Giulio Schimperna, Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 6, pp. 1431–1454

DOI 10.1016/J.ANIHPC.2015.05.006