一维量子Navier-Stokes方程组的指数衰减

摘要

In this paper,we study the long-time asymptotics of solutions of the quantum Navier-Stokes equations in one space dimension.By using the equivalence of the quantum NavierStokes equations to the viscous quantum Euler system and the entropy dissipation method,we prove that the particle density converges exponentially fast to the constant thermal equilibrium state as the time tends to infinity.In Theorem 1.1 of the paper,we give the convergence rate to this steady state.%本文研究了一维量子Navier-Stokes方程组解的长时间渐近性.利用量子Navier-Stokes方程组与粘性量子欧拉方程组的等价性以及熵耗散化方法,证明了当时间趋于无穷大时粒子浓度以指数的速度趋于常数热平衡状态.本文的定理1.1给出了其稳态收敛率.