学术报告
报告题目：Supersonic polytropic van der Waals gas around a concave corner
报告时间：2025年11月14日 10:00-11:00
报 告 人：郭俐辉 新疆大学教授
腾讯会议：623-110-206
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报告摘要：
The supersonic flow around a concave corner has been pointed out by Courant and Friedrichs in their monographs as one of the most important problems in fluid dynamics. For the pproblem of an ideal gas turning a concave corner, when the inclination wall is smaller than a critical angle, Prandtl firstly used the method of shock polar to demonstrate that two types of shocks are generated at the corner: one is a weak shock, and the other is a strong shock.
In this talk, we investigate the two-dimensional steady supersonic incoming flow turning a concave corner with a polytropic van der Waals gas.We obtain a series of novel multi-solutions structures, such as a centered compressible simple wave or a strong non-sonic shock; a weak left sonic shock, and so on. Compared to an ideal gas, the polytropic van der Waals gas flow around a concave corner exhibits richer physical phenomena due to its non-convex nature, presenting challenges to research. To address these difficulties, we employ the methods of convex hull, shock polar of a polytropic van der Waals gas, and perturbed inclined solid walls. Furthermore, we prove the composite wave solutions, the left sonic shock solution and the non-sonic shock solution are stable under small perturbations of the inclined solid wall.
报告人简介：
郭俐辉，教授，博士生导师，美国数学评论评论员，主要从事非线性守恒律方程组的理论研究。先后主持国家自然科学基金4项，主持省部级项目2项，在JDE, ZAMP,JMP,POF等杂志上发表多篇论文。