JournalspmVol. 64 / No. 1DOI 10.4171/pm/1778

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 -solutions for large initial data and then show the large-time behavior of -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.