報(bào)告題目： Sonic-supersonic solutions for the 3D steady full ultra-relativistic Euler equations with axial-symmetry

報(bào)告人：范永強(qiáng)

報(bào)告時(shí)間： 2025年06月10日下午 16:00-17:00

報(bào)告地點(diǎn)：騰訊會(huì)議：939-876-316

會(huì)議密碼：021591

報(bào)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, ?, ?). Next, utilizing characteristic decomposition and the hodograph transformation (t, ξ) → (cos?, ?)(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.

報(bào)告人簡(jiǎn)介：

范永強(qiáng)，新疆大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院副教授、碩士生導(dǎo)師。2022年于新疆大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院取得博士學(xué)位。研究方向?yàn)殡p曲型偏微分方程理論及其應(yīng)用。在J. Differ. Equ，Z. Angew. Math. Phys，Nonlinear Anal. Real World Appl，Math. Methods Appl. Sci. 等雜志上發(fā)表論文5篇。主持新疆青年科學(xué)基金1項(xiàng)、新疆“天池英才”青年博士項(xiàng)目1項(xiàng)。