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

✍ Scribed by Fei Jiang

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
189 KB
Volume
12
Category
Article
ISSN
1468-1218

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✦ Synopsis

In [A. Jüngel, Global weak solutions to compressible Navier-Stokes equations for quantum fluids, SIAM J. Math. Anal. 42 (2010) 1025-1045], Jüngel 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 Jüngel'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 Jüngel'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.

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