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Entropy-bounded solutions to the compressible Navier-Stokes equations: with far field vacuum. (arXiv:1710.06571v1 [math.AP])
来源于:arXiv
The entropy is one of the fundamental states of a fluid and, in the viscous
case, the equation that it satisfies is highly singular in the region close to
the vacuum. In spite of its importance in the gas dynamics, the mathematical
analyses on the behavior of the entropy near the vacuum region, were rarely
carried out; in particular, in the presence of vacuum, either at the far field
or at some isolated interior points, it was unknown if the entropy remains its
boundedness. The results obtained in this paper indicate that the ideal gases
retain their uniform boundedness of the entropy, locally or globally in time,
if the vacuum occurs at the far field only and the density decays slowly enough
at the far field. Precisely, we consider the Cauchy problem to the
one-dimensional full compressible Navier-Stokes equations without heat
conduction, and establish the local and global existence and uniqueness of
entropy-bounded solutions, in the presence of vacuum at the far field only. It
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