Brown University: 2007.7–
Professor: 2017.6–
Associate Professor: 2012.7–2017.6
Assistant Professor: 2007.7–2012.6
Member of the Lefschetz Center for Dynamical Systems.
University of Pennsylvania: 2010.9–2010.12
Visiting scholar (Sabbatical).
Institute for Advanced Study: 2006.9–2007.6, 2008.9–2008.12
Member & Visiting Scholar.
Mathematical Sciences Research Institute: 2007.7–2007.8
Member of ”Summer Microprogram on Nonlinear Partial Differential Equations”.
University of Chicago: 2005.9–2006.8
L.E. Dickson Instructor & Research post-doctor
University of Minnesota: 2001.9–2005.8.
Research Assistant & Teaching Assistant
Kim, Doyoon, Dong, Hongjie, Zhang, Hong Neumann problem for non-divergence elliptic and parabolic equations with BMO$_x$ coefficients in weighted Sobolev spaces. Discrete and Continuous Dynamical Systems. 2016; 36 (9) : 4895-4914. |
Cho, Sungwon, Dong, Hongjie, Kim, Doyoon Boundary Value Problems for Parabolic Operators in a Time-Varying Domain. Communications in Partial Differential Equations. 2015; 40 (7) : 1282-1313. |
Dong, Hongjie, Zhang, Hong Conormal problem of higher-order parabolic systems with time irregular coefficients. Trans. Amer. Math. Soc.. 2015; 368 (10) : 7413-7460. |
Dong, Hongjie, Kim, Doyoon Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces. Advances in Mathematics. 2015; 274 : 681-735. |
Ammari, H., Dong, H., Kang, H., Kim, S. On An Elliptic Equation Arising from Photo-Acoustic Imaging in Inhomogeneous Media. International Mathematics Research Notices. 2015; |
Dong, Hongjie, Xiong, Jingang Boundary Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates. International Mathematics Research Notices. 2014; 2015 (17) : 7734-7756. |
Dong, Hongjie, Gu, Xumin Boundary partial regularity for the high dimensional Navier–Stokes equations. Journal of Functional Analysis. 2014; 267 (8) : 2606-2637. |
Dong, Hongjie, Li, Dong Global $${{dot{H}^1 cap dot{H}^{-1}}}$$ H ˙ 1 ∩ H ˙ - 1 Solutions to a Logarithmically Regularized 2D Euler Equation. J. math. fluid mech.. 2014; 17 (1) : 1-7. |
Dong, Hongjie, Kim, Seick Green's functions for parabolic systems of second order in time-varying domains. Communications on Pure and Applied Analysis. 2014; 13 (4) : 1407-1433. |
Li, Dong, Dong, Hongjie On a generalized maximum principle for a transport-diffusion model with $log$-modulated fractional dissipation. Discrete and Continuous Dynamical Systems. 2014; 34 (9) : 3437-3454. |
Dong, Hongjie On a multi-dimensional transport equation with nonlocal velocity. Advances in Mathematics. 2014; 264 : 747-761. |
Dong, Hongjie, Kim, Doyoon
On the impossibility of |
Dong, Hongjie, Kim, Doyoon Parabolic Equations in Simple Convex Polytopes with Time Irregular Coefficients. SIAM Journal on Mathematical Analysis. 2014; 46 (3) : 1789-1819. |
Dong, Hongjie, Gu, Xumin Partial regularity of solutions to the four-dimensional Navier-Stokes equations. Dynamics of Partial Differential Equations. 2014; 11 (1) : 53-69. |
Dong, Hongjie, Zhang, Hong Schauder estimates for higher-order parabolic systems with time irregular coefficients. Calculus of Variations and Partial Differential Equations. 2014; 54 (1) : 47-74. |
Dong, Hongjie, Li, Dong On a one-dimensional $alpha $-patch model with nonlocal drift and fractional dissipation. Trans. Amer. Math. Soc.. 2013; 366 (4) : 2041-2061. |
Dong, Hongjie On elliptic equations in a half space or in convex wedges with irregular coefficients. Advances in Mathematics. 2013; 238 : 24-49. |
Dong, Hongjie, Krylov, N. V. On the Existence of Smooth Solutions for Fully Nonlinear Parabolic Equations with Measurable “Coefficients” without Convexity Assumptions. Communications in Partial Differential Equations. 2013; 38 (6) : 1038-1068. |
Dong, Hongjie Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates. Archive for Rational Mechanics and Analysis. 2012; 205 (1) : 119-149. |
Dong, Hongjie, Kim, Doyoon On -estimates for a class of non-local elliptic equations. Journal of Functional Analysis. 2012; 262 (3) : 1166-1199. |
Dong, Hongjie, Krylov, N. V., Li, Xu On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains. St. Petersburg Math. J.. 2012; 24 (1) : 39-69. |
Dong, Hongjie, Strain, Robert M. On partial regularity of steady-state solutions to the 6D Navier-Stokes equations. Indiana University Mathematics Journal. 2012; 61 (6) : 2211-2229. |
Dong, H. Parabolic equations with variably partially VMO coefficients. St. Petersburg Math. J.. 2012; 23 (3) : 521-539. |
Dong, Hongjie, Kim, Doyoon Schauder estimates for a class of non-local elliptic equations. Discrete and Continuous Dynamical Systems. 2012; 33 (6) : 2319-2347. |
Dong, Hongjie Solvability of second-order equations with hierarchically partially BMO coefficients. Trans. Amer. Math. Soc.. 2012; 364 (1) : 493-517. |
Cho, Sungwon, Dong, Hongjie, Kim, Seick Global Estimates for Green’s Matrix of Second Order Parabolic Systems with Application to Elliptic Systems in Two Dimensional Domains. Potential Analysis. 2011; 36 (2) : 339-372. |
Dong, Hongjie, Kim, Doyoon Global Regularity of Weak Solutions to Quasilinear Elliptic and Parabolic Equations with Controlled Growth. Communications in Partial Differential Equations. 2011; 36 (10) : 1750-1777. |
Dong, Hongjie, Kim, Doyoon Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains. Journal of Functional Analysis. 2011; 261 (11) : 3279-3327. |
Dong, Hongjie On Similarity Solutions to the Multidimensional Aggregation Equation. SIAM Journal on Mathematical Analysis. 2011; 43 (4) : 1995-2008. |
Dong, Hongjie, Kim, Doyoon Parabolic and Elliptic Systems in Divergence Form with Variably Partially BMO Coefficients. SIAM Journal on Mathematical Analysis. 2011; 43 (3) : 1075-1098. |
Dong, Hongjie The Aggregation Equation with Power-Law Kernels: Ill-Posedness, Mass Concentration and Similarity Solutions. Commun. Math. Phys.. 2011; 304 (3) : 649-664. |
Dong, Hongjie, Kim, Doyoon L p solvability of divergence type parabolic and elliptic systems with partially BMO coefficients. Calculus of Variations and Partial Differential Equations. 2010; 40 (3-4) : 357-389. |
Dong, Hongjie, Li, Dong On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces. Journal of Differential Equations. 2010; 248 (11) : 2684-2702. |
Dong, Hongjie, Kim, Doyoon On the L p -Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients. Archive for Rational Mechanics and Analysis. 2010; 199 (3) : 889-941. |
Dong, Hongjie, Kim, Seick Partial Schauder estimates for second-order elliptic and parabolic equations. Calculus of Variations and Partial Differential Equations. 2010; 40 (3-4) : 481-500. |
Dong, Hongjie, Krylov, N. V. Second-order elliptic and parabolic equations with $B(mathbb{R}^{2}, VMO)$ coefficients. Trans. Amer. Math. Soc.. 2010; 362 (12) : 6477-6477. |
Dong, Hongjie Solvability of parabolic equations in divergence form with partially BMO coefficients. Journal of Functional Analysis. 2010; 258 (7) : 2145-2172. |
Dong, Hongjie, Pavlović, Nataša A regularity criterion for the dissipative quasi-geostrophic equations. Annales de l'Institut Henri Poincare (C) Non Linear Analysis. 2009; 26 (5) : 1607-1619. |
Dong, Hongjie Dissipative quasi-geostrophic equations in critical Sobolev spaces: Smoothing effect and global well-posedness. Discrete and Continuous Dynamical Systems. 2009; 26 (4) : 1197-1211. |
Dong, Hongjie, Kim, Doyoon Elliptic Equations in Divergence Form with Partially BMO Coefficients. Archive for Rational Mechanics and Analysis. 2009; 196 (1) : 25-70. |
Dong, Hongjie, Du, Dapeng, Li, Dong Finite time singularities and global well-posedness for fractal Burgers equations. Indiana University Mathematics Journal. 2009; 58 (2) : 807-822. |
Dong, Hongjie, Kim, Seick Green’s matrices of second order elliptic systems with measurable coefficients in two dimensional domains. Trans. Amer. Math. Soc.. 2009; 361 (06) : 3303-3303. |
Dong, Hongjie, Li, Dong Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations. Communications in Mathematical Sciences. 2009; 7 (1) : 67-80. |
Dong, Hongjie, Kim, Doyoon Parabolic and Elliptic Systems with VMO Coefficients. Methods and Applications of Analysis. 2009; 16 (3) : 365-388. |
Dong, Hongjie, Pavlović, Nataša Regularity Criteria for the Dissipative Quasi-Geostrophic Equations in Hölder Spaces. Commun. Math. Phys.. 2009; 290 (3) : 801-812. |
Dong, Hongjie, Du, Dapeng The Navier-Stokes Equations in the Critical Lebesgue Space. Commun. Math. Phys.. 2009; 292 (3) : 811-827. |
Dong, Hongjie, Li, Dong Finite time singularities for a class of generalized surface quasi-geostrophic equations. Proceedings of the American Mathematical Society. 2008; 136 (07) : 2555-2563. |
Du, Dapeng, Dong, Hongjie Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discrete and Continuous Dynamical Systems. 2008; 21 (4) : 1095-1101. |
Cho, Sungwon, Dong, Hongjie, Kim, Seick On the Green's matrices of strongly parabolic systems of second order. Indiana University Mathematics Journal. 2008; 57 (4) : 1633-1678. |
Dong, Hongjie, Kim, Seick, Safonov, Mikhail On Uniqueness of Boundary Blow-Up Solutions of a Class of Nonlinear Elliptic Equations. Communications in Partial Differential Equations. 2008; 33 (2) : 177-188. |
Dong, Hongjie, Li, Dong Spatial Analyticity of the Solutions to the Subcritical Dissipative Quasi-geostrophic Equations. Archive for Rational Mechanics and Analysis. 2008; 189 (1) : 131-158. |
Dong, Hongjie Well-posedness for a transport equation with nonlocal velocity. Journal of Functional Analysis. 2008; 255 (11) : 3070-3097. |
Dong, Hongjie, Krylov, N. V. On time-inhomogeneous controlled diffusion processes in domains. The Annals of Probability. 2007; 35 (1) : 206-227. |
Dong, Hongjie, Du, Dapeng Partial Regularity of Solutions to the Four-Dimensional Navier-Stokes Equations at the First Blow-up Time. Commun. Math. Phys.. 2007; 273 (3) : 785-801. |
Dong, Hongjie, Krylov, Nicolai V. The Rate of Convergence of Finite-Difference Approximations for Parabolic Bellman Equations with Lipschitz Coefficients in Cylindrical Domains. Applied Mathematics and Optimization. 2007; 56 (1) : 37-66. |
Dong, Hongjie, Staubach, Wolfgang Unique continuation for the Schrödinger equation with gradient vector potentials. Proceedings of the American Mathematical Society. 2007; 135 (07) : 2141-2150. |
Dong, Hongjie Hessian Equations with Elementary Symmetric Functions. Communications in Partial Differential Equations. 2006; 31 (7) : 1005-1025. |
Dong, Hongjie, Du, Dapeng On the Local Smoothness of Solutions of the Navier–Stokes Equations. J. math. fluid mech.. 2006; 9 (2) : 139-152. |
Dong, Hongjie About smoothness of solutions of the heat equations in closed, smooth space-time domains. Communications on Pure and Applied Mathematics. 2005; 58 (6) : 799-820. |
Year | Degree | Institution |
---|---|---|
2005 | PhD | University of Minnesota |
2001 | BS | Fudan University |
NSF Grant: DMS-1600593 (P.I.), 2016.7 to 2019.6.
NSF CAREER Award: DMS-1056737 (P.I.), 2011.7 to 2016.6.
NSF Grant: DMS-0800129 (P.I.), 2008.7 to 2012.6.
MSRI Membership: 2007.7 to 2007.8.
IAS Membership: 2006 to 2007, 2008.9 to 2008.12.
Travel Grant from AMS for ICM 2006, Madrid, Spain: August 22 to 30, 2006.
Outstanding Graduate: Fudan University, 2001.
The First, Second Prizes of People's Scholarship: Fudan University, 1998 to 2001.
Meritorious Winner of Mathematical Contest in Modeling: The Consortium for Mathematics and its Applications, 2000.
Perfect Paper on the American Invitational Mathematics Examination: The Mathematical Association of America, 1997.
The First Prize of Chinese Mathematical Olympiad: rank top 4 in P.R.China, 1997.
The First, Second Prizes: in contests of Mathematics, Physics and Chemistry, 1991 to 1997.
Name | Title |
---|---|
Rozovsky, Boris | Ford Foundation Professor Emeritus of Applied Mathematics, Professor of Applied Mathematics (Research) |
APMA 2110 - Real Analysis |
APMA 2120 - Hilbert Spaces and Their Applications |
APMA 2240 - Partial Differential Equations |