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报告题目：Well-Posedness and Phase Transition Mechanisms in Compressible Fluid Systems with the van der Waals Equation of State
报 告 人：施小丁，北京化工大学 教授
报告摘要：This work presents two studies on compressible fluids governed by the van der Waals equation of state: (1) A refined \(L^2\)-energy framework is developed to establish the global well-posedness of the compressible non-isentropic Navier–Stokes system, yielding bounded physical quantities and global strong solutions. (2) For the periodic problem of the steady isentropic Navier–Stokes system, phase transitions are shown to depend on pressure non-monotonicity and the integral average of specific volume. An artificial viscosity approximation is employed to demonstrate convergence either to equilibrium or to a non-transition state. Overall, pressure non-monotonicity, together with a suitable condition on specific volume, serves as a nucleation mechanism for phase transitions.
报告人简介：施小丁，北京化工大学教授。博士毕业于中国科学院数学与系统科学研究院，曾在日本大阪大学从事博士后研究。主要研究可压缩Navier-Stokes方程及其相关问题的适定性、大时间行为、奇异极限等。 主要学术论文发表在 CMP、SIMA、IUMJ、JMFM、Nonlinearity，JDE等刊物。主持和参加多项国家自然科学基金及省部级基金项目。
报告时间：2026年4月14日 15：00-18：00
报告地点：文渊楼 B119
主办单位：数学与统计学院
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