Royal Society Newton Fellow
Research Associate of Keble College
+44 1865 273566
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
My research focuses on the mathematical theory of partial differential equations (PDE) in fluid dynamics and General relativity, which includes the well-posedness, singularity formation, and the vanishing viscosity limit of smooth or weak solutions for the compressible Navier-Stokes equations (CNS), the compressible Euler equations (CE), Einstein-Euer equations and some multi-physics process in fluid dynamics such as Magnetohydrodynamics (MHD) and Radiation hydrodynamics (RHD).
Joint Ph.D, Georgia Institute of Technology, USA,
Sep., 2012 -- Sep., 2014,
Advisor: Prof. Ronghua Pan.
Ph.D, Shanghai Jiao Tong University, China,
Sep., 2009 -- Sep., 2012; Sep., 2014 -- Jun., 2015.
Advisor: Yachun Li.
Research Assistant, The Chinese University of Hong Kong, HK,
Aug., 2015 -- Aug., 2017,
Mentor: Prof. Zhouping Xin.
Research Fellow, Monash University, Australia,
Aug., 2017-- Mar., 2018,
Mentor: Prof. Todd A. Oliynyk.
Now I am a research associate in Keble college, and Newton International Fellowships in Mathematical Insititute. My supervisor is Prof. Gui-Qiang Chen.
Prizes, awards, and scholarships:
China Scholarship, China Scholarship Council, China, 2012;
Qiu Shi Scholarship, Qiu Shi Science and Technologies Foundation, Hong Kong, 2014;
Newton International Fellowships, Royal Society, UK, 2017.
Major / recent publications:
- Formation of singularities and existence of global continuous solution for the compressible Euler equations, joint with Geng Chen and Gui-Qiang G. Chen, 2019, submitted, https://arxiv.org/abs/1905.07758.
- Formation of singularities for the relativistic Euler equations, joint with Nikolaus Athanasiou, 2019, submitted, https://arxiv.org/abs/1903.03355v2.
- Global well-posedness of regular solutions to the three-dimensional compressible Navier-Stokes Equations with degenerate viscosities and vacuum, joint with Zhouping Xin, 2018, submitted, https://arxiv.org/abs/1806.02383.
- Well-posedness of three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum, joint with Zhouping Xin, 2018, submitted, https://arxiv.org/pdf/1811.04744.
- Dynamical liquid bodies in general relativity, joint with Todd A. Oliynyk, 2018, prepare.
- Minimum principle of the temperature in three-dimensional compressible flow with vacuum, joint with Geng Chen and Weizhe Zhang, 2016, submitted.
- On classical solutions for viscous polytropic fluids with degenerate viscosities and vacuum, joint with Yachun Li and Ronghua Pan, to appear in Arch. Rational Mech. Anal., 2019, https://arxiv.org/abs/1503.05644.
- Vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow with vacuum, joint with Yongcai Geng and Yachun Li, to appear in Arch. Rational Mech. Anal., 2019, https://link.springer.com/article/10.1007/s00205-019-01401-9.
- A polygonal scheme and the lower bound on density for the isentropic gas dynamics, joint with Geng Chen and Ronghua Pan, DCDS-A 39(7) (2019), 4259-4277.
- Blow-up criterion for the 3D non-resistive compressible Magnetohydrodynamic equation, joint with Shuai Xi, 2019, J. Dynam. Differential Equations, https://link.springer.com/article/10.1007/s10884-019-09756-z.
- On classical solutions to 2D Shallow water equations with degenerate viscosities, joint with Yachun Li and Ronghua Pan, J. Math. Fluid Mech., 19 (2017), no. 1, 151–190.
- Vanishing Viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow with far field vacuum, joint with Min Ding, J. Math. Pure. Appl., (9) 107 (2017), no. 3, 288–314.
Existence results and blow-up criterion of compressible radiation hydrodynamic equations, joint with Yachun Li, J. Dynam. Differential Equations, 29 (2017), no. 2, 549–595.
Singularity formation for compressible Euler equations, joint with Geng Chen and Ronghua Pan, SIAM. J. Math. Anal., 2017.
- On classical solutions of the compressible Magnetohydrodynamic equations with vacuum, SIAM. J. Math. Anal., 47 (2015) 2722-2753.
Recent progress on classical solutions for compressible isentropic Navier-Stokes equations with degenerate viscosities and vacuum, joint with Yachun Li and Ronghua Pan, Bull. Braz. Math. Soc. (N.S.) 47 (2016), 507-519.
No BV bounds for approximate solutions to p-system with general pressure law, joint with Alberto Bressan, Geng Chen, Qingtian Zhang, J. Hyperbolic Differential Equations 12(2015) 799-816.
Existence results for viscous polytropic fluids with degenerate viscosity coefficients and vacuum, J. Differential Equations 259 (2015) 84-119.
On regular solutions of the 3D compressible isentropic Euler-Boltzmann equations with vacuum, joint with Yachun Li, Disc. Cont. Dyna. Syst. (A) 35 (2015), 3059-3086.
Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum, joint with Yachun Li, J. Differential Equations 256 (2014) 3943-3980.