TY  - JOUR
AU  - Kong, Chunxiang
AU  - Feng, Xiaofang
PY  - 2026
TI  - Global existence of solutions to a non-isentropic compressible diffuse interface model
JO  - AIMS Mathematics
SP  - 17093
EP  - 17114
VL  - 11
IS  - 6
AB  - 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.
UR  - https://doi.org/10.3934/math.2026700
DO  - 10.3934/math.2026700