Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 642-651.

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Existence of Global Strong Solutions for Initial Value Problems of One-Dimensional Compressible Navier-Stokes Equations

Shangxi Guo()   

  1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070
  • Received:2019-05-24 Online:2021-06-01 Published:2021-06-09


To consider the initial problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity. By using the energy estimates, the lower and upper bounds for the density is derived, that is, nether vacuum states nor concentration states can occur. Finally, the approximate solution is constructed by transforming the viscous coefficient, the existence of global strong solution is obtained by using the local existence conclusion of the strong solution and combining a prior estimates of the density function and the velocity function.

Key words: Navier-Stokes equation, Compressible, Global strong solution, Density-dependent viscosity

CLC Number: 

  • O175.29