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Stability of the rarefaction wave for a coupled compressible Navier‐Stokes/Allen‐Cahn system
Author(s) -
Luo Ting,
Yin Haiyan,
Zhu Changjiang
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4925
Subject(s) - rarefaction (ecology) , compressibility , mathematics , allen–cahn equation , navier–stokes equations , mathematical analysis , energy method , energy (signal processing) , stability (learning theory) , mechanics , physics , computer science , ecology , statistics , machine learning , species diversity , biology
In this paper, we are concerned with the large time behavior of solutions to the Cauchy problem for the one dimensional Navier‐Stokes/Allen‐Cahn system. Motivated by the relationship between the Navier‐Stokes/Allen‐Cahn system and the Navier‐Stokes system, we can prove that the solutions to the one‐dimensional compressible Navier‐Stokes/Allen‐Cahn system tend time‐asymptotically to the rarefaction wave, where the strength of the rarefaction wave is not required to be small. The proof is mainly based on a basic energy method.