袁源
研究方向: 流体偏微分方程的数学理论研究
yyuan2102@m.scnu.edu.cn

教育背景

2015.09–2018.08   博士,香港中文大学数学系,导师:辛周平 教授

2013.08–2015.08 硕士,香港中文大学数学系,导师:辛周平 教授

2009.09–2013.06 学士,数学与应用数学专业,吉林大学
 

工作经历

2022.12 – 至今        副研究员,数学科学学院,华南师范大学
2019.05 – 2020.03   博士后,布雷西亚大学, 导师:Paolo Secchi 教授
2018.09 – 2022.11   讲师,华南数学应用与交叉研究中心/数学科学学院,华南师范大学

 

开设课程

2023-2024,数学分析(二)
2023-2024,数学分析(一)
2022-2023,高等数学(上)
2021-2022,高等数学(上)

科研项目

  1. 2021.01--2023.12   含真空情形的可压Navier-Stokes方程的有界熵解的存在性问题;广东省自然科学基金面上项目;主持
  2. 2020.01.01--2022.12.31: 非等熵气体方程的真空自由界面问题的一些研究;国家自然科学基金青年科学基金项目;主持

学术成果

  1. X. Liu, Y. Yuan: Immediate blowup of entropy-bounded classical solutions to the vacuum free boundary problem of nonisentropic compressible Navier–Stokes equations. SIAM J. Math. Anal. 51(2023), no.3, 1524-1544.
  2. Y. Yuan: Variational rotating solutions to non-isentropic Euler-Poisson equations with prescribed total mass. Sci. China. Math. 65 (2022), 2061-2078.
  3. P. Secchi, Y. Yuan: Weakly nonlinear surface waves on the plasma-vacuum interface.  J. Math. Pures Appl. (9) 163 (2022), 132–203. 
  4. Q. Yuan, Y. Yuan: Periodic perturbations of a composite wave of two viscous shocks for 1-D full compressible Navier-Stokes equations. SIAM J. Math. Anal. 54 (2022), no. 3, 2876–2905.
  5. Z. Xin, Q. Yuan, Y. Yuan: Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws.  Indiana Univ. Math. J. 70 (2021), no. 6, 2295–2349. 
  6. Q. Yuan, Y. Yuan: On Riemann solutions under different initial periodic perturbations at two infinities for 1-d scalar convex conservation laws. J. Differential Equations 268 (2020), no. 9, 5140–5155.
  7. X. Liu, Y. Yuan: The self-similar solutions to full compressible Navier-Stokes equations without heat conductivity. Math. Models Methods Appl. Sci. 29 (2019), no. 12, 2271–2320.
  8. Z. Xin, Q. Yuan, Y. Yuan: Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-d convex scalar viscous conservation laws. SIAM J. Math. Anal. 51 (2019), no. 4, 2971–2994.
  9. X. Liu, Y. Yuan: Local existence and uniqueness of strong solutions to the free boundary problem of the full compressible Navier-Stokes Equations in three dimensions. SIAM J. Math. Anal. 51(2019), no.2, 748–789.

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