Electron. J. Differential Equations, Vol. 2026 (2026), No. 78, pp. 1-27.

Incompressible limit for non-isentropic compressible Euler-Navier-Stokes two-phase flow model in R^3

Chol-Ung Rim, Hakho Hong

Abstract:
This article concerns the incompressible limit for the two-phase flow model consisting of the compressible isothermal Euler equations coupled with compressible non-isentropic Navier-Stokes equations through a drag forcing term. For the 3D Cauchy problem, we rigorously justify the incompressible limits, which mean that the solutions converge to that of a compressible Euler/incompressible Navier-Stokes system and a compressible Euler/non-homogeneous incompressible Navier-Stokes system as Mach number goes to zero, under the small and large temperature variations, respectively.

Submitted July 14, 2025. Published October 1, 2026.
Math Subject Classifications: 35Q30, 35B35, 35L65, 76D33, 74J40.
Key Words: Euler-Navier-Stokes two-phase flow; low Much number limit; small temperature variation; large temperature variation.
DOI: 10.58997/ejde.2026.78

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Chol-Ung Rim
Department of Mathematics
University of Sciences
Pyongyang, DPR Korea
email: rimcu@star-co.net.kp
Hakho Hong
Institute of Mathematics
State Academy of Sciences
Pyongyang, DPR Korea
email: hhhong@star-co.net.kp

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