TY - JOUR
T1 - Global Existence of Weak Solutions to the Three-Dimensional Full Compressible Quantum Equations
AU - Guo , Boling
AU - Xie , Binqiang
JO - Annals of Applied Mathematics
VL - 1
SP - 1
EP - 31
PY - 2022
DA - 2022/06
SN - 34
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20559.html
KW - global weak solution, compressible quantum Navier-Stokes
equations, thermal conduction.
AB - <p style="text-align: justify;">We consider the quantum Navier-Stokes equations for the viscous, compressible, heat conducting fluids on the three-dimensional torus $T^3.$ The model
is based on a system which is derived by Jungel, Matthes and Milisic [15]. We
made some adjustment about the relation of the viscosities of quantum terms.
The viscosities and the heat conductivity coefficient are allowed to depend on
the density, and may vanish on the vacuum. By several levels of approximation we prove the global-in-time existence of weak solutions for the large initial
data.</p>