Acta mathematica scientia, Series B >
CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS
Received date: 2011-11-17
Online published: 2012-01-20
Supported by
The research of R.X. Lian is supported by NSFC (11101145). The research of H.L. Li is partially supported by NSFC (10871134, 11171228), the Huo Ying Dong Fund (111033), the Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR201006107). The research of L. Xiao is supported by NSFC (11171327).
We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coe?cient. For regular initial data, we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically. When initial density is piecewise regular with jump discontinuity, we show that there exists a unique global piecewise regular solution. In
particular, the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t → +∞.
Key words： Navier-Stokes equations; discontinuous initial data
LIAN Ru-Xu , LIU Jian , LI Hai-Liang , XIAO Ling . CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 315 -324 . DOI: 10.1016/S0252-9602(12)60019-8
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