JournalspmVol. 64 , No. 1pp. 87–126

On the Cauchy problem for a one-dimensional compressible viscous polytropic ideal gas

  • Yuming Qin

    Donghua University, Shanghai, China
  • Yumei Wu

    Baylor University, Waco, United States
  • Fagui Liu

    Water Conservancy and Hydroelectric Power, Zhengzhou, China
On the Cauchy problem for a one-dimensional compressible viscous polytropic ideal gas cover

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Abstract

In this paper, we first prove the regularity and continuous dependence on initial data for HiH^i-solutions (i=1,2,4)(i=1,2,4) for large initial data and then show the large-time behavior of Hi(i=2,4)H^i(i=2,4)-global solutions for small initial data to the Cauchy problem for the compressible Navier--Stokes equations of a one-dimensional viscous polytropic ideal gas. Moreover, we also obtain the large-time behavior of ``small'' classical solutions {\em in the norm of classical solutions} for this model.

Cite this article

Yuming Qin, Yumei Wu, Fagui Liu, On the Cauchy problem for a one-dimensional compressible viscous polytropic ideal gas. Port. Math. 64 (2007), no. 1 pp. 87–126

DOI 10.4171/PM/1778