报告题目： Sonic-supersonic solutions for the 3D steady full ultra-relativistic Euler equations with axial-symmetry
报告人：范永强
报告时间： 2025年06月10日下午 16:00-17:00
报告地点：腾讯会议：939-876-316
会议密码：021591
报告摘要：
Sonic-supersonic solutions are significant for establishing the piecewise smooth solutions to the ultra-relativistic transonic flow problem. Under the condition of non-swirl, the problem is transformed into proving the existence of a classical solution for a boundary value problem (BVP) of 4×4 hyperbolic system with two independent variables. The difficulty in addressing this issue arises from the parabolic degeneracy of the equations on the sonic boundary coupled with the emergence of singularities. To overcome this difficulty, inspired by Hu and Li [Sonic-supersonic solutions for the two-dimensional steady full Euler equations, Arch. Ration. Mech. Anal., 2020], transforming the 3D axisymmetric steady full URE equations without swirl into an equivalent system with variables (S, B, ϑ, ϖ). Next, utilizing characteristic decomposition and the hodograph transformation (t, ξ) → (cosϖ, ϑ)(x, r), we further transform the system into a 3×3 closed first-order hyperbolic system with a distinct singularity-regularity structure. Subsequently, the existence of a local classical solution for the BVP of 3×3 system is proved in a weighted metric space. Finally, using the invertibility of the hodograph transformation, a sonic-supersonic solution on the original physical plane is obtained.
报告人简介：
范永强，新疆大学数学与系统科学学院副教授、硕士生导师。2022年于新疆大学数学与系统科学学院取得博士学位。研究方向为双曲型偏微分方程理论及其应用。在J. Differ. Equ，Z. Angew. Math. Phys，Nonlinear Anal. Real World Appl，Math. Methods Appl. Sci. 等杂志上发表论文5篇。主持新疆青年科学基金1项、新疆“天池英才”青年博士项目1项。
