GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

In this article, we are concerned with the global weak solutions to the 1D compressible viscous hydrodynamic equations with dispersion correction δ;ρ((φ（ρ）)xxφ′（ρ）)x withφ（ρ） = ρα. The model consists of viscous stabilizations because of quantum Fokker-Planck operator in the Wigner equation and is supplemented with periodic boundary and initial conditions. The diffusion term εu xx in the momentum equation may be interpreted as a classical conservative friction term because of particle interactions. We extend the existence result in[1]（α =1/2） to 0 < α≤1. In addition, we perform the limit ε→ 0 with respect to 0 < α≤1/2.