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Zero dissipation limit to rarefaction wave with vacuum for the micropolar compressible flow with temperature‐dependent transport coefficients
Author(s) -
Gong Guiqiong
Publication year - 2020
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.7110
Subject(s) - rarefaction (ecology) , zero (linguistics) , dissipation , compressibility , mathematics , limit (mathematics) , mathematical analysis , compressible flow , mechanics , thermal conduction , thermodynamics , physics , ecology , philosophy , linguistics , species diversity , biology
In this article, we consider the zero dissipation limit of the micropolar equations with temperature‐dependent viscosity and heat‐conduction coefficient. If the given rarefaction wave to the corresponding conservation systems connects to vacuum at one side, we can construct a sequence of solutions to the micropolar equations which converge to the given rarefaction wave with vacuum as the transport coefficients tend to zero. And the uniform convergence rate can be obtained. The key point in our analysis is how to control the degeneracies of the density, the temperature, and the temperature‐dependent viscosities at the vacuum region in the zero dissipation limit process.