I am currently an associate professor (tenure track) at Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences in Beijing, China.
My research is mainly focused on the partial differential equations in fluid dynamics, especially for the nonlinear stability of wave phenomena in gas dynamics.
Qian Yuan
qyuan@amss.ac.cn
Academy of Mathematics and Systems Science
Chinese Academy of Sciences
55, Zhongguancun East Road
Haidian District, Beijing
China
Projects
- 2023.01-2025.12: National Natural Science Foundation of China (PI, ongoing).
- 2022.10-2027.12: CAS Project for Young Scientists in Basic Research (Participant, ongoing).
- 2022.01-2026.12: Youth Innovation Promotion Association of Chinese Academy of Sciences (PI, ongoing).
- 2019.08-2021.06: Fellowships of China Postdoctoral Science Foundation (PI, completed).
Publications
Preprints- Yuan, Qian; Zhao, Wenbin. The incompressible limit of viscous vortex sheets with large data. Preprint.
- Huang, Feimin; Xin, Zhouping; Xu, Lingda; Yuan, Qian. Nonlinear asymptotic stability of compressible vortex sheets with viscosity effects. arXiv:2308.06180.
- Yuan, Qian. Time-asymptotic stability of planar Navier-Stokes shocks with spatial oscillations. accepted by SCIENCE CHINA Mathematics, arXiv:2212.13414.
- Yuan, Qian. Planar Viscous Shocks with Periodic Perturbations for Scalar Multidimensional Viscous Conservation Laws. SIAM J. Math. Anal. 55 (2023), no. 3, 1499-1523.
- Huang, Feimin; Xu, Lingda; Yuan, Qian. Asymptotic stability of planar rarefaction waves under periodic perturbations for 3-d Navier-Stokes equations. Adv. Math. 404 (2022), Paper No. 108452, 27 pp..
- Yuan, Qian; Yuan, 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.
- Huang, Feimin; Yuan, Qian. Stability of planar rarefaction waves for scalar viscous conservation law under periodic perturbations. Methods Appl. Anal. 28 (2021), no. 3, 337–353.
- Xin, Zhouping; Yuan, Qian; Yuan, Yuan. Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-D convex scalar viscous conservation laws. Indiana Univ. Math. J. 70 (2021), no. 6, 2295–2349.
- Huang, Feimin; Yuan, Qian. Stability of large-amplitude viscous shock under periodic perturbation for 1-d isentropic Navier-Stokes equations. Comm. Math. Phys. 387 (2021), no. 3, 1655–1679.
- Yuan, Qian; Yuan, 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.
- Xin, Zhouping; Yuan, Qian; Yuan, Yuan Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws. SIAM J. Math. Anal. 51 (2019), no. 4, 2971–2994.
Teaching
- 2024 spring: Lecturer, 180080070102P4011Z ``Applied Partial Differential Equations''.