Lei Li received his B.S. in mathematics and physics in 2010 at Tsinghua University, and got his Ph.D. in mathematics from University of Wisconsin-Madison in 2015. Before joining INS, Lei worked as a postdoc in the Department of Mathematics at Duke University from 2015 to 2018.
Dr. Lei Li’s research interest lies in Applied Mathematics. The topics include analysis of differential equations, fluid-structure interaction, numerical PDEs and SDEs.
- Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations. Communications in Mathematical Sciences, Accepted. Yuanyuan Feng, Lei Li, Jian-Guo Liu.
- Some compactness criteria for weak solutions of time fractional PDEs. SIAM Journal on Mathematical Analysis. In press. Lei Li, Jian-Guo Liu.
- A generalized definition of Caputo derivatives and its application to fractional ODEs. SIAM Journal on Mathematical Analysis. 50(3) 2867-2900, 2018. Lei Li, Jian-Guo Liu.
- Cauchy problems for Keller-Segel type time-space fractional diffusion equation. Journal of Differential Equations;256(3) 1044-1096, 2018; Lei Li, Jian-Guo Liu, Lizhen Wang.
- p-Euler equations and p-Navier-Stokes equations. Journal of Differential Equations; 264(7), 4707-4748, 2018; Lei Li, Jian-Guo Liu.
- Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem. Journal of Statistical Physics, 169(2) 361-339, 2017; Lei Li, Jian-Guo Liu, Jianfeng Lu.
- Swimming and pumping by helical waves in viscous and viscoelastic fluids Physics of Fluids, 27(2), 2015; Lei Li, Saverio Spagnolie.
- The sedimentation of flexible filaments. Journal of fluid mechanics, 735, 705-736, 2013; Lei Li, H. Manikantan, David Saintillan, Saverio Spagnolie.