Bird-Carreau型黏性van der Waals流体周期解的渐近稳定性

讨论了一维可压缩黏性van der Waals流体系统的渐近稳定性，其中黏性系数为满足Bird-Carreau模型的非线性函数，压力为非凸函数。通过构造能量函数并运用能量估计方法及单调算子理论，证明得出：大黏性条件下初值位于稳定区域时，以及大黏性、小扰动条件下初值位于亚稳定区域时，该类van der Waals流体的解是渐近稳定的。
Abstract：In this paper, the asymptotic stability of a one-dimensional compressible viscous van der Waals fluids system is discussed, where the viscosity coefficient is a nonlinear function that satisfies the Bird-Carreau model, and the pressure is a non-convex function. By constructing the energy function and using the energy estimation method and the monotone operator theory, we prove that:under the condition of large viscosity, the solutions of the non-Newtonian fluid are asymptotically stable when the initial value is either located in the stable region, or located in the metastable region under small disturbance conditions.