Stability of the Rarefaction Wave for a Non-isentropic Navier-Stokes/Allen-Cahn System*


Ting LUO.Stability of the Rarefaction Wave for a Non-isentropic Navier-Stokes/Allen-Cahn System*[J].Chinese Annals of Mathematics B,2022,43(2):233~252
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Ting LUO;


National Natural Science Foundation of China (No. 12001249), the Natural Science Foundation of Jiangxi Province of China (No. GJJ190280) and the Scientific Research Funds of Jiangxi University of Finance and Economics (No. 012270624).
Abstract: This paper is concerned with the large time behavior of solutions to the Cauchy problem for a one-dimensional compressible non-isentropic Navier-Stokes/Allen-Cahn system which is a combination of the classical Navier-Stokes system with an Allen-Cahn phase field description. Motivated by the relationship between Navier-Stokes/Allen-Cahn and Navier-Stokes, the author can prove that the solutions to the one dimensional compressible non-isentropic 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.


Navier-Stokes/Allen-Cahn system, Rarefaction wave, Stability


35M10, 35B40, 35B35
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