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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2007, Vol. 8 Issue (10): 1681-1690    DOI: 10.1631/jzus.2007.A1681
Computational Mathematics     
Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity
ZHANG Ting, FANG Dao-yuan
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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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.

Key words： Compressible Navier-Stokes equations      Vacuum states      Density-dependent viscosity     
Received: 14 November 2006     
CLC:  O175  
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ZHANG Ting
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Cite this article:

ZHANG Ting, FANG Dao-yuan. Non-formation of vacuum states for Navier-Stokes equations with density-dependent viscosity. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1681-1690.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2007.A1681     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2007/V8/I10/1681

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