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Local well‐posedness of compressible radiation hydrodynamic equations with density‐dependent viscosities and vacuum
Author(s) -
Li Hao,
Li Yachun
Publication year - 2021
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.7064
Subject(s) - mathematics , compressibility , isentropic process , viscosity , initial value problem , mathematical analysis , volume viscosity , compressible flow , cauchy problem , mechanics , physics , thermodynamics
In this paper, we consider the Cauchy problem for three‐dimensional isentropic compressible radiation hydrodynamic equations with density‐dependent viscosity coefficients. When the viscosity coefficients are given as power of density ( ρ δ with δ > 1 ), we establish the local‐in‐time existence of classical solutions containing a vacuum for large initial data. Here, we point out that the initial layer compatibility conditions are not necessary.