Summary of the Tianyuan Mathematical Research Center Workshop on "Mathematical Theory of Compressible Flow 2025"
The Tianyuan Mathematical Research Center Workshop on "Mathematical Theory of Compressible Flow 2025" was successfully held from July 13 to 19, 2025. The workshop was organized by Professor Feimin Huang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences) and Professor Yong Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences). The event brought together 19 participants from various universities and research institutions both within China and internationally. Attendees included leading experts in the field of compressible fluids, innovative young scholars, and promising doctoral students. Presentations covered the latest advances and future directions in the mathematical theory of compressible flow.
The seminar aims to build an open, interactive and efficient communication platform, so that participants can deeply explore the frontier issues of mathematical theory of compressible fluids and jointly promote the prosperity and development of this discipline. The seminar mainly focuses on core issues such as singular solutions of high-dimensional compressible Euler equations, exchanges the latest research results and development trends, and deeply explores the research trends of high-dimensional compressible fluids and their theoretical connections with related fields. It drives theoretical research with problems and promotes the theoretical development of compressible fluids and related problems, and improves the ability to use modern mathematical methods to deal with compressible fluids and related problems. This academic seminar brings together compressible fluid mechanics equations such as Euler equations, magnetohydrodynamic equations, and quantum fluid equations. Experts and scholars at the meeting held heated discussions and exchanges on research directions such as shock wave canonical reflection problems, Radon measure solutions, supersonic fluids, and the fluid dynamics limit of the Boltzmann equation, and identified important and challenging directions for future research.
This conference has carefully planned 12 academic reports, covering a wide range of frontier areas of compressible fluids and related issues. There are some very representative research works: Professor Yongqian Zhang of Fudan University reported the latest progress in the results of some direct and inverse problems of steady supersonic flow through wedges or curved walls. Professor Hairong Yuan of East China Normal University taught the unsteady compressible Euler flow rotating around a fixed solid in three-dimensional space. There may be an infinitely thin layer with concentrated mass, and characterized this phenomenon by proposing the concept of Randon measure solution. Professor Beixiang Fang of Shanghai Jiaotong University elaborated on the transonic shock wave solution of the steady three-dimensional axisymmetric Euler flow with rotational velocity in a finite cylindrical pipe, and revealed that the rotational velocity plays a crucial role. Professor Wei Xiang of City University of Hong Kong presented the latest results on the potential flow equation and the canonical reflection of the shock wave of the Euler equation. In addition, many scholars including Professor Aifang Qu from Shanghai Normal University, Professor Tianyi Wang from Wuhan University of Technology, Professor Tao Wang from Wuhan University, and Professor Jianfeng Cheng from Sichuan University presented research reports on related topics such as the singular Riemann problem of the compressible Euler equation, the pressure vanishing limit of the isentropic Euler equation, the vacuum free boundary problem of the ideal compressible magnetohydrodynamic equation, and the well-posedness problem of steady incompressible jets with vorticity and gravity. The scholars conducted in-depth discussions on related issues and provided valuable insights.
This conference intends to invite researchers at different levels in the field of compressible fluids and related fields to share and exchange the latest research results and urgent problems in the field. This academic event has the following significance:
(1) This conference has greatly promoted academic exchanges and built a platform for communication and collaboration for experts and scholars from different research directions of compressible fluids and related issues. By in-depth discussion of research results, exchange of academic insights, sharing of experience and results, the conference not only promoted the discussion of future research trends and directions of compressible fluids, but also promoted the cross-integration with other related research (e.g., statistical physics, quantum theory), which helped to condense major and key scientific issues in the research field.
(2) The conference has played a positive role in promoting academic progress in compressible fluids and related fields. It provides scholars with an opportunity to conduct in-depth research in their own fields, enabling them to be exposed to core issues in cutting-edge theories, modern methods, and the latest developments of related research teams in a short period of time. Through academic exchanges, scholars combined their respective research results and jointly expanded further research directions, thereby promoting cutting-edge academic progress in their fields.
(3) This conference also provides young scholars with an opportunity to grow rapidly. The conference provides a platform for young teachers and doctoral students to have close contact with top international scholars, enabling young scholars to understand cutting-edge international topics and the latest research progress. Through exchanges and encouragement between participants from different directions, levels, and schools, young scholars can broaden their research horizons and enhance their learning motivation.
All participants expressed great appreciation for the world-class research and exchange platform provided by Tianyuan Mathematics Research Center, and also gave consistent high recognition to the excellent service and comprehensive assistance provided by the center's staff. The new research ideas inspired by this academic event will be reflected in the researchers' academic achievements, and we would like to express our sincere gratitude.