@article{Kong2026, 
author = {Chunxiang Kong and Xiaofang Feng},
title = {Global existence of solutions to a non-isentropic compressible diffuse interface model},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17093-17114},
keywords = {Navier–Stokes/Allen–Cahn system, global existence, uniqueness, non-isentropic, compressible diffuse interface},
url = {https://www.sciopen.com/article/10.3934/math.2026700},
doi = {10.3934/math.2026700},
abstract = {In this paper, we investigate the existence of solutions to a class of compressible Navier–Stokes/Allen–Cahn systems describing the motion of a mixture of two viscous compressible fluids. Using the energy method and refined interpolation inequalities, we establish the global existence of solutions in the Sobolev spaces        H          i       for    i  =  2  ,  4. The system features a temperature-dependent heat conductivity    k  (  θ  )  =      θ    β   with    β  >  0, which characterizes the flow of a two-phase immiscible, thermally viscous, compressible fluid mixture. The main technical difficulty of this work lies in the complicated estimates induced by high-order partial derivatives in the proof of solution regularity.}
}