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

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Date
2014
Volume
1966
Issue
Journal
Series Titel
WIAS Preprints
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Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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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 [12] where existence of weak solutions was proved in three space dimensions. Here, we aim at studying 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 [12]. Moreover, we can admit slightly more general conditions on some material coefficients of the system.

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