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Volume 34, Issue 1
Global Existence of Weak Solutions to the Three-Dimensional Full Compressible Quantum Equations

Boling Guo & Binqiang Xie

Ann. Appl. Math., 34 (2018), pp. 1-31.

Published online: 2022-06

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  • Abstract

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.

  • Keywords

global weak solution, compressible quantum Navier-Stokes equations, thermal conduction.

  • AMS Subject Headings

76E25, 76E17, 76W05, 35Q35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-34-1, author = {Guo , Boling and Xie , Binqiang}, title = {Global Existence of Weak Solutions to the Three-Dimensional Full Compressible Quantum Equations}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {34}, number = {1}, pages = {1--31}, abstract = {

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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20559.html} }
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 -

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.

Guo , Boling and Xie , Binqiang. (2022). Global Existence of Weak Solutions to the Three-Dimensional Full Compressible Quantum Equations. Annals of Applied Mathematics. 34 (1). 1-31. doi:
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