报告题目 (Title)：Steady-state Solution to the One-Dimensional Isothermal van der Waals Model with Phase Transition(一维等温范德瓦尔斯模型相变的稳态解)
报告人 (Speaker)：施小丁 教授 (北京化工大学)
报告时间 (Time)：2025年11月11日（周二） 14:00 pm
报告地点 (Place)：腾讯会议 290 457 116
邀请人(Inviter)：朱佩成
报告摘要：In this talk, we investigate the well-posedness of the steady-state compressible Navier–Stokes system with the van der Waals equation of state. The main difficulty lies in the non-monotonicity of the van der Waals equation, which leads to the liquid-vapor phase transition, resulting in physical instability and multiple solutions in mathematics. We have shown that the multiplicity of solutions depends on whether the average density lies within the gas-liquid coexistence region (i.e., the Maxwell construction). In particular, by introducing an artificial viscosity term, we constructed an approximate equation for this problem. When the average density falls within the Maxwell region, the solution converges to the two equilibrium states given by Maxwell's construction as the artificial viscosity tends to zero. Consequently, the continuous transition through a diffusion interface is replaced by a discontinuous jump in the limit of vanishing viscosity. When the initial state is outside the Maxwell region, the approximate solution and its limit always remain within that region. Research shows that the instability caused by the non-monotonicity of pressure can serve as the nucleus for phase separation. The approximate solution constructed in this work can be regarded as a smoothed approximation for the solution of the phase change problem.