The long-time behavior of the particle density of the compressible quantum Navier-Stokes equations in one space dimension is studied. It is shown that the particle density converges exponentially fast to the constant ...The long-time behavior of the particle density of the compressible quantum Navier-Stokes equations in one space dimension is studied. It is shown that the particle density converges exponentially fast to the constant thermal equilibrium state as the time tends to infinity, the decay rate is also obtained. The results hold regardless of either the bigger of the scaled Planck constant or the viscosity constant. This improves the decay results of [5] by removing the crucial assumption that the scaled Planck constant is bigger than the viscosity constant. The proof is based on the entropy dissipation method and the Bresch-Desjardins type of entropy.展开更多
基金Supported by the National Natural Science Foundation of China(No.11501525)the Natural Science Foundation of Henan Province Science and Technology Department(162300410077)+1 种基金the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province(2013GGJS-142)the Youth Natural Science Foundation of Zhengzhou University of Aeronautics(2015113001)
文摘The long-time behavior of the particle density of the compressible quantum Navier-Stokes equations in one space dimension is studied. It is shown that the particle density converges exponentially fast to the constant thermal equilibrium state as the time tends to infinity, the decay rate is also obtained. The results hold regardless of either the bigger of the scaled Planck constant or the viscosity constant. This improves the decay results of [5] by removing the crucial assumption that the scaled Planck constant is bigger than the viscosity constant. The proof is based on the entropy dissipation method and the Bresch-Desjardins type of entropy.
