A remark on weak solutions to the barotropic compressible quantum Navier-Stokes equations

In [A. Jungel, Global weak solutions to compressible Navier-Stokes equations for quantum fluids, SIAM J. Math. Anal. 42 (2010) 1025-1045], Jungel proved the global existence of the barotropic compressible quantum Navier-Stokes equations for when the viscosity constant is bigger than the scaled Planck constant. Recently, Dong [J. Dong, A note on barotropic compressible quantum Navier-Stokes equations, Nonlinear Anal. TMA 73(2010)854-856] extended Jungel's result to the case where the viscosity constant is equal to the scaled Planck constant by using a new estimate of the square root of the solutions. In this paper we show that jungel's existence result still holds when the viscosity constant is bigger than the scaled Planck constant. Consequently, with our result, the existence for all physically interesting cases of the scaled Planck and viscosity constants is obtained. (C) 2010 Elsevier Ltd. All rights reserved.