Hongjie Dong
Brown University · Applied Mathematics
Active 2005–2026
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About
Hongjie Dong is a Professor of Applied Mathematics at Brown University. He earned his Ph.D. in Mathematics from the University of Minnesota in 2005. His research interests encompass three main areas: partial differential equations, where he focuses on nonlinear elliptic and parabolic PDEs, Navier-Stokes equations, quasi-geostrophic equations, reaction diffusion equations, and unique continuation problems; probability, with an emphasis on the probabilistic approach to PDEs, stochastic processes, and stochastic control theory; and numerical analysis, particularly the rates of convergence of finite difference approximations. Dr. Dong has received several awards and honors, including the NSF Career Award from 2011 to 2016, and has been a member of MSRI and IAS. His academic background includes recognition as an outstanding graduate and multiple prizes in mathematical contests during his early education in China.
Research topics
- Mathematics
- Mathematical analysis
- Pure mathematics
- Applied mathematics
- Physics
Selected publications
Hessian estimates for equations involving p-Laplacian via a fundamental inequality
Advances in Mathematics · 2020-05-28 · 30 citations
article1st authorTime analyticity for the heat equation and Navier-Stokes equations
Journal of Functional Analysis · 2020-04-09 · 26 citations
article1st authorCorrespondingSharp Material Interface Limit of the Darcy–Boussinesq System
SIAM Journal on Applied Mathematics · 2025-08-07 · 2 citations
article1st authorCorrespondingMathematische Annalen · 2025-10-31 · 1 citations
article1st authorCorrespondingInterior and boundary mixed norm derivative estimates for nonstationary Stokes equations
Communications in Contemporary Mathematics · 2025-06-13 · 1 citations
article1st authorCorrespondingIn this paper, we obtain weighted mixed norm Sobolev estimates in the whole space for nonstationary Stokes equations in divergence and nondivergence form with variable viscosity coefficients that are merely measurable in time variable and have small mean oscillation in spatial variables in small cylinders. As an application, we prove interior mixed norm derivative estimates for solutions to both equations. We also discuss boundary mixed norm Hessian estimates for solutions to equations in nondiv…
Recent grants
CAREER: Problems in regularity theory for linear and nonlinear partial differential equations
NSF · $545k · 2011–2017
Research topics in partial differential equations
NSF · $150k · 2008–2012
Topics in Regularity Theory of Partial Differential Equations
NSF · $325k · 2016–2019
Frequent coauthors
- 77 shared
Doyoon Kim
- 42 shared
Zongyuan Li
City University of Hong Kong
- 42 shared
Jongkeun Choi
- 33 shared
Seick Kim
- 30 shared
Tuoc Phan
University of Tennessee at Knoxville
- 23 shared
Zhuolun Yang
Providence College
- 22 shared
Н. В. Крылов
- 22 shared
Longjuan Xu
Capital Normal University
Education
- 2005
Ph.D., Mathematics
University of Minnesota
- 2001
BS, Mathematics
Fudan University
Awards & honors
- NSF Career Award (2011-2016)
- MSRI Membership: 2007.7–2007.8
- IAS Membership: 2006–2007
- Travel Grants from AMS for ICM 2006, Madrid, Spain: August 2…
- Outstanding Graduate: Fudan University, 2001
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