Van der Waals型流体相变问题的渐近稳定性

Asymptotic stability of the solution of a model system for van der Waals fluids

研究了van der Waals流体动力学方程组,通过引入人工黏性和周期边界条件,给出了此类流体方程组解的渐近稳定性。计算了带人工黏性的定常解问题,通过局部解的存在唯一性分析和先验估计,证明了定常解在全局范围内的渐近稳定性。

A model system of van der Waals fluids has been investigated, and the asymptotic stability of the solution has been established for a periodic boundary value problem with artificial viscosity. A solution of steady-state periodic boundary value problem has also been derived. By means of the existence and uniqueness of the local solution and the priori estimates, the steady-state solution is shown to have asymptotic stability.