Abstract
The purpose of this paper is to present our recent progress on the local theory of classical solutions for compressible isentropic Navier-Stokes equations with density dependent viscosities in a power law and vacuum, which is a long-standing open problem due to the very high degeneracy caused by vacuum for this system. We will also mention some related open problems of high mathematical interest for this system.
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Li, Y., Pan, R. & Zhu, S. Recent progress on classical solutions for compressible isentropic Navier-Stokes equations with degenerate viscosities and vacuum. Bull Braz Math Soc, New Series 47, 507–519 (2016). https://doi.org/10.1007/s00574-016-0165-7
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DOI: https://doi.org/10.1007/s00574-016-0165-7