AI 中文总结
针对一维可压缩等熵Navier-Stokes系统在范德华物态方程下的两相共存相变容许稳态解，本文构造半离散交错网格差分格式，通过先验估计证明周期边值问题解的全局存在性，确立了这类相变解在一般小扰动下的非线性稳定性。
AI 中文摘要
本文研究一维空间中，可压缩等熵Navier-Stokes系统在范德华物态方程下周期边值问题的某些稳态解的动态稳定性。这些稳态解对应描述两相共存相变的容许解，其中比容的积分平均值属于麦克斯韦区域。我们首先构造半离散交错网格差分格式，证明周期问题解的局部存在性，且无需施加标准稳定性假设\
英文摘要
In this paper, we investigate the dynamic stability of certain steady-state solutions to the periodic boundary value problem for compressible isentropic Navier-Stokes system under the van der Waals equation of state in one space dimension. These steady-state solutions correspond to the admissible solutions describing two-phase coexisting phase transitions, where the integral average of the specific volume belongs to the Maxwell region. We first construct a semi-discrete staggered grid difference scheme to prove the local existence of solutions to the periodic problem, without imposing the standard stability hypothesis \(p_v<0\). Then, by virtue of rigorous piecewise a priori estimates, we demonstrate that the periodic boundary value problem for van der Waals fluids possesses a global solution existing for all time, and this solution converges uniformly to the admissible steady state as time tends to infinity. This result firmly establishes the nonlinear stability of the admissible phase-transition solutions under general small initial disturbances.
Comments29 pages, 3 figures
