WIAS Preprint No. 1966, (2014)

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


  • Eleuteri, Michela
  • Rocca, Elisabetta
    ORCID: 0000-0002-9930-907X
  • Schimperna, Giulio

2010 Mathematics Subject Classification

  • 35Q35 35K25 76D05 35D30


  • Cahn-Hilliard, Navier-Stokes, incompressible non-isothermal binary fluid, global-in-time existence, a-priori estimates




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 citeERS 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 citeERS. Moreover, we can admit slightly more general conditions on some material coefficients of the system.

Appeared in

  • Ann. Inst. H. Poincare Anal. Non Lineaire, 33: 6 (2016), pp. 1431--1454

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