\bibitem{NSAC-FS} G.~Favre and G.~Schimperna, {\sl On a Navier-Stokes-Allen-Cahn model with inertial effects}, J.~Stat.~Phys, \href{https://link.springer.com/article/10.1007/s10955-020-02503-5}{doi: doi.org/10.1007/s10955-020-02503-5}, (2020).