Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (1): 157-181.doi: 10.1016/S0252-9602(14)60148-X

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ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS

FANG Li,LI ZiLai   

  1. CNS and Department of Mathematics, Northwest University, Xi’an 710127, China
  • Received:2013-12-10 Revised:2014-04-21 Online:2015-01-20 Published:2015-01-20
  • Supported by:

    Supported by NSFC (11201371, 1331005), and Natural Science Foundation of Shaanxi Province (2012JQ020).

Abstract:

In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.

Key words: compressible non-Newtonian fluids, vacuum, local classical solution

CLC Number: 

  • 76N10
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