Zhongwei Shen, Ph. D.
▎Professor of Mathematics
▎Partial Differential Equations and Harmonic Analysis
◢ Email：shenzhongwei@westlake.edu.cn
To help Westlake University become a top research university.
Biography
Zhongwei Shen earned his B.S. in Mathematics from Peking University in 1982 at the age of eighteen. He went on to complete his M.S. at the Institute of Mathematics, Chinese Academy of Sciences in 1985, and received his Ph.D. in Mathematics from the University of Chicago in 1989. Dr. Shen began his academic career with positions at Princeton University and Purdue University before joining the University of Kentucky in 1995. He was promoted to Professor in 2003 and served as Chair of the Department of Mathematics from 2007 to 2011. He joined the Institute for Theoretical Sciences, Westlake University as a Professor of Mathematics in July 2025.
Dr. Shen is a member of the inaugural class of American Mathematical Society Fellows and was named a Distinguished Professor in the College of Arts and Sciences at the University of Kentucky in 2016.
Research
Shen's research lies at the interface of harmonic analysis, partial differential equations, and mathematical physics. He is particularly interested in boundary value problems in non-smooth domains, the homogenization theory, spectral properties of Schrödinger operators，and Navier-Stokes equations. He developed a new real-variable method, which produced the best-known results for the solvability of the Lp boundary value problems for elliptic systems in Lipschitz domains. Together with his collaborators, he established the optimal uniform regularities for boundary value problems in elliptic homogenization. He also introduced a new scaling function, which has played a critical role in the study of Schrödinger operators with electric and magnetic potentials.
Representative Publications
1) J. Geng and Z. Shen, Resolvent Estimates in L∞ for the Stokes Operator in Nonsmooth Domains, Inventiones Mathematicae.
2) F. Lin and Z. Shen, Critical Sets of Solutions of Elliptic Equations in Periodic Homogenization, Comm. Pure Appl. Math. 77 (7), pp.3143-3183 (2024).
3) Z. Shen and J. Zhuge, Regularity of Homogenized Boundary Data in Periodic Homogenization of Elliptic Systems, J. Eur. Math. Soc. (JEMS) 22 (9), pp.2751-2776 (2020).
4) Z. Shen and J. Zhuge, Boundary Layers in Periodic Homogenization of Neumann Problems, Comm. Pure Appl. Math.71 (11), pp.2163-2219 (2018).
5) S. N. Armstrong and Z. Shen, Lipschitz Estimates in Almost-Periodic Homogenization, Comm. Pure Appl. Math.69 (10), pp.1882-1923 (2016).
6) C. Kenig, F. Lin, and Z. Shen, Periodic Homogenization of Green and Neumann Functions, Comm. Pure Appl. Math. 67 (8), pp.1219-1262 (2014).
7) C. Kenig, F. Lin, and Z. Shen, Homogenization of Elliptic Systems with Neumann Boundary Conditions, J. Amer. Math. Soc.26 (4), pp.901-937 (2013).
8) Z. Shen, Resolvent Estimates in Lp for the Stokes Operator in Lipschitz Domains, Arch. Ration. Mech. Anal. 205 (2), pp.395-424 (2012).
9) C. Kenig and Z. Shen, Layer Potential Methods for Elliptic Homogenization Problems, Comm. Pure Appl. Math. 64 (1), pp.1-44 (2011).
10) Z. Shen, The Lp Boundary Value Problems on Lipschitz Domains, Adv. Math.216 (1), pp.212-254 (2007).
11) Z. Shen, On Absolute Continuity of the Periodic Schrödinger Operators, Internat. Math. Res. Notices 2001 (1), pp.1-32 (2001).
12) Z. Shen, Lp Estimates for Schrödinger Operators with Certain Potentials, Ann. Inst. Fourier (Grenoble) 45 (2), pp.513-546 (1995).
13) Z. Shen, Boundary Value Problems for Parabolic Lame Systems and a Nonstationary Linearized System of Navier-Stokes Equations in Lipschitz Cylinders, Amer. J. of Math.113 (2), pp.293-373 (1991).
Contact Information
Email：shenzhongwei@westlake.edu.cn
Postdoc Position
https://its.westlake.edu.cn/info/1024/3019.htm
