Stability of the rarefaction wave for a coupled compressible Navier‐Stokes/Allen‐Cahn system | Zendy

Luo Ting | Zendy; Yin Haiyan | Zendy; Zhu Changjiang | Zendy

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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.

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