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

TL;DR

This paper proves the existence of global strong solutions for a two-dimensional nonisothermal diffuse interface model describing two-phase flows of incompressible fluids, extending previous three-dimensional results.

Contribution

It establishes the existence of global strong solutions in 2D and allows more general conditions on material coefficients, advancing the mathematical understanding of the model.

Findings

Existence of global in time strong solutions in 2D

More general conditions on material coefficients

Extension of previous 3D results to 2D

Abstract

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of weak solutions in three space dimensions. Here, we aim at studying the mathematical properties of the model in the two-dimensional case. In particular, we can show existence of global in time strong solutions. Moreover, we can admit slightly more general conditions on some material coefficients of the system.