In this article, we are concerned with the global weak solutions to the 1D compressible viscous hydrodynamic equations with dispersion correction δ2ρ((ϕ(ρ))xxϕ'(ρ))x with ϕ(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 εuxx 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.
Boling GUO
,
Xiaoyu XI
. GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2017
, 37(3)
: 573
-583
.
DOI: 10.1016/S0252-9602(17)30023-1
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