On the Cauchy problem for a one-dimensional compressible viscous polytropic ideal gas (Q2466284)

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