Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 72, pp. 1-22.

Title: Existence of solutions for a non-isothermal Navier-Stokes-Allen-Cahn
system with thermo-induced coefficients
       
Authors: Juliana Honda Lopes (Univ. Estadual de Campinas, SP, Brazil)
         Gabriela Planas (Univ. Estadual de Campinas, SP, Brazil)
         
Abstract: 
This article aims to study the existence of solutions for a non-isothermal
Navier-Stokes-Allen-Cahn system with thermo-induced coefficients.
The system can be considered as a model describing the motion of a mixture of
two viscous incompressible fluids with viscosity, thermal conductivity and
interfacial thickness being temperature-dependent.
 This is a more general system than the previous ones considered in the literature,
involving temperature dependence on all main coefficients.
The strong non-linear couplings between those equations because of the temperature
dependence brings new mathematical difficulties that only allows working in two
dimensions.

Submitted May 20, 2022. Published October 25, 2022.
Math Subject Classifications: 35K51, 35A02, 35Q35.
Key Words: Nonlinear system; Navier-Stokes-Allen-Cahn system; non-isothermal
           phase-field.