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

You need to subscribe to download the article.

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.