On the Cauchy problem for a one-dimensional compressible viscous polytropic ideal gas
Yuming Qin
Donghua University, Shanghai, ChinaYumei Wu
Baylor University, Waco, United StatesFagui Liu
Water Conservancy and Hydroelectric Power, Zhengzhou, China
![On the Cauchy problem for a one-dimensional compressible viscous polytropic ideal gas cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-pm-volume-64-issue-1.png&w=3840&q=90)
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 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