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Local well-posedness of compressible Radiation Hydrodynamic equations with density-dependent viscosities and vacuum
  • Hao Li,
  • Yachun Li
Hao Li
Shanghai Jiao Tong University
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Yachun Li
Shanghai Jiao Tong University
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Peer review status:UNDER REVIEW

18 May 2020Submitted to Mathematical Methods in the Applied Sciences
23 May 2020Assigned to Editor
23 May 2020Submission Checks Completed
23 May 2020Reviewer(s) Assigned

Abstract

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 ($\rho^\delta$ with $\delta>1$), 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.