Sonic-supersonic solutions for the 3D steady full ultra-relativistic Euler equations with axial-symmetry
报告专家：范永强 副教授（新疆大学）
报告时间：12月6日（星期六）上午10:10-10:50
报告地点：国家天元数学西南中心401
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.
专家简介：
范永强，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. 等杂志上发表论文数篇。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。
邀请人：何躏
