Communications in Mathematical Sciences
Volume 21 (2023)
Sharp interface limit for compressible Navier–Stokes/Allen–Cahn system with shock wave
Pages: 1487 – 1503
In this paper, the sharp interface limit for the diffusion interface model system of immiscible two-phase flow called compressible Navier–Stokes/Allen–Cahn system is studied in one dimension. The results show that, for the initial perturbations with small energy but possibly large oscillations of shock wave solutions, and the strength of initial phase field is allowed to vary arbitrarily within its physical meaning, then the sharp interface limit of the compressible Navier–Stokes/Allen–Cahn system is the standard two-phase compressible Navier–Stokes equations.
compressible Navier–Stokes equations, Allen–Cahn equation, shock wave, stability, sharp interface limit
2010 Mathematics Subject Classification
35B40, 35B65, 35C20, 35M10, 35Q35, 76N10, 76T30
This paper is supported by the National Natural Science Foundation of China (Nos. 12171024, 11971217, 11971020), Natural Science Foundation of Jiangxi Province (No. 20202ACBL211002), Academic and Technical Leaders Training Plan of Jiangxi Province (No. 20212BCJ23027).
Received 24 July 2022
Received revised 24 July 2022
Accepted 9 November 2022
Published 22 September 2023