GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

doi:10.1016/S0252-9602(17)30023-1

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (3): 573-583.doi: 10.1016/S0252-9602(17)30023-1

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GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

Boling GUO¹, Xiaoyu XI²

1. Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China;
2. The Graduate School of China Academy of Engineering Physics, P. O. Box 2101 Beijing 100088, China

Received:2016-03-31 Online:2017-06-25 Published:2017-06-25
Supported by:
This work was supported by NSF (11271052).

Abstract

Abstract: 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)=ρ^α. 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.

Key words: Viscous hydrodynamic equations, global weak solution, dispersion correction, periodic boundary and initial conditions

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.

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GLOBAL WEAK SOLUTIONS TO ONE-DIMENSIONAL COMPRESSIBLE VISCOUS HYDRODYNAMIC EQUATIONS

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