学术报告会：Steady-State Solutions for a 1D Isothermal van der Waals Fluid with Phase Transition

报告题目：Steady-State Solutions for a 1D Isothermal van der Waals Fluid with Phase Transition

报 告 人： 施小丁（北京化工大学    教授）

报告时间：2026年1月29日周四10:10

报告地点：S3-313

Abstract：In this talk, we examine the well-posedness of the steady, compressible, isentropic Navier-Stokes equations with van der Waals pressure and periodic boundaries. The central issue is pressure non-monotonicity, responsible for phase transitions and resulting in solution non-uniqueness. Solution multiplicity coincides with the averaged specific volume lying in the Maxwell coexistence region. Through an artificial viscosity approximation, we show that inside this region, solutions converge to the two Maxwell equilibria as viscosity vanishes, forming a sharp interface; outside, they stay outside. Thus, non-monotonic pressure nucleates phase separation, and our method regularizes the transition description.

个人简介：

施小丁，北京化工大学教授，博士生导师，1996年博士毕业于中国科学院数学与系统科学研究院。主要研究领域为流体力学方程组的相关问题，包括可压缩Navier-Stokes方程组的波的叠加、碰撞等大时间行为；非牛顿不可压缩Navier-Stokes方程组固液耦合问题和混合边值问题解的适定性及数值分析等。部分成果发表在数学领域的重要杂志Comm. Math. Phys., Indiana Univ. Math. J., SIAM J. Math. Anal., Nonlinearity, J. Differential Equations等，多次主持和参与国家自然科学基金项目。