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Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity
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ZHANG Ting, FANG Dao-yuan. Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1681-1690.
@article{title="Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity",
author="ZHANG Ting, FANG Dao-yuan",
journal="Journal of Zhejiang University Science A",
volume="8",
number="10",
pages="1681-1690",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1681"
}
%0 Journal Article
%T Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity
%A ZHANG Ting
%A FANG Dao-yuan
%J Journal of Zhejiang University SCIENCE A
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%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A1681
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T1 - Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity
A1 - ZHANG Ting
A1 - FANG Dao-yuan
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 10
SP - 1681
EP - 1690
%@ 1673-565X
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1681
Abstract: We consider the Cauchy problem, free boundary problem and piston problem for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. Using the reduction to absurdity method, we prove that the weak solutions to these systems do not exhibit vacuum states, provided that no vacuum states are present initially. The essential requirements on the solutions are that the mass and energy of the fluid are locally integrable at each time, and the Lloc1-norm of the velocity gradient is locally integrable in time.
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