A note on barotropic compressible quantum Navier-Stokes equations

作者：Dong Jianwei^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(4): 854-856.

DOI：10.1016/j.na.2010.03.047

• Compressible quantum Navier-Stokes equations
• Viscous quantum Euler equations
• Global existence

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations has been proved very recently, by Jungel (2009) [1], if the viscosity constant is smaller than the scaled Plank constant. This paper extends the results to the case that the viscosity constant equals the scaled Plank constant. By using a new estimate on the square root of the solution, apparently not available in [1], the semiclassical limit for the viscous quantum Euler equations (which are equivalent to the barotropic compressible quantum Navier-Stokes equations) can be performed; then the results of this paper are obtained easily.

• 出版日期2010-8-15
• 单位郑州航空工业管理学院