Global weak solutions to the Navier-Stokes equations for a 1D viscous polytropic ideal gas
We prove the existence of global weak solutions to the Navier-Stokes equations for a one-dimensional viscous polytropic ideal gas. We require only that the initial density is in L°°r\Lfoc with positive infimum, the initial velocity is in Lfoc, and the initial temperature is in Lloc with positive infimum. The initial density and the initial velocity may have differing constant states at x = ±00. In particular, piecewise constant data with arbitrary large jump discontinuities are included. Our results show that neither vacuum states nor concentration states can form and the temperature remains positive in finite time.