Yuan Yuan

School of Mathematical Sciences
associate professor
Field:Mathematical theory of partial differential equations in fluids
     yyuan2102@m.scnu.edu.cn

2015.09 -- 2018.08    Ph.D. The Chinese University of Hong Kong.
2013.08 -- 2015.08    M.Phil. The Chinese University of Hong Kong.
2009.09 -- 2013.06     Bachelor. Jilin University.
 

2022.12 -- Present    Associate Research Fellow, School of Mathematical Sciences, South China Normal University
2019.05 -- 2020.03   Postdoc, University of Brescia
2018.09 -- 2022.11   Assistant Research Fellow, CAMIS/School of Mathematical Sciences, South China Normal University
 

1. Q. Yuan, Y. Yuan: Shock waves with non-localized perturbations for 1D scalar convex conservation laws. Methods Appl. Anal. 32 (2026), no. 4, 331-344.
2. Y. Li, Y. Mei, Y. Yuan: Asymptotic stability of shock profiles and rarefaction waves to the Navier-Stokes-Poisson system under space-periodic perturbations. J. Differential Equations 420 (2025), no. 9, 5140–5155.
3. 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.
4. Y. Yuan: Variational rotating solutions to non-isentropic Euler-Poisson equations with prescribed total mass. Sci. China. Math. 65 (2022) 2061-2078.
5. P. Secchi, Y. Yuan: Weakly nonlinear surface waves on the plasma-vacuum interface.  J. Math. Pures Appl. (9) 163 (2022), 132–203. 
6. 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.
7. 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. 
8. 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.
9. 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.
10. 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.
11. 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.