Hongjie Dong, Publications

About smoothness of solutions of the heat equations in closed smooth space-time domains, Comm. Pure Appl. Math. 58 (2005) no. 6, 799-820.

On the rate of convergence of finite-difference approximations for Bellman's equations with constant coefficients, with N.V. Krylov, Algebra i Analis (St. Petersburg Math. J.) 17 (2005), no. 2, 108-132.

On the local smoothness of solutions of the Navier-Stokes equations, with D. Du, J.Math. Fluid Mech. 9 (2007), no. 2, 139-152.

Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with C1 and C2 coefficients, with N.V. Krylov, Electro. J. Differential Equations 2005 (2005), no. 102, 1-25.

On some problems related to the regularity theory for second-order elliptic-parabolic equations and their numerical approximations, Ph.D thesis (2005), advisor: N.V. Krylov.

Hessian equations with elementary symmetric functions, Comm. Partial Differential Equations. 31 (2006) no. 7, 1005-1025.

On time inhomogeneous controlled diffusion processes in domains, with N.V. Krylov, Annal. Prob. 35, no. 1 (2007), 206-227.

On the rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients in domains, with N.V. Krylov, Appl. Math. Optim., 56,(2007) no. 1, 37-66.

On unique continuation for the schrödinger equation with gradient vector potentials, with W. Staubach, Proc. Amer. Math. Soc. 135 (2007), no. 7, 2141-2149.

On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equations, with S. Kim and M.V. Safonov, Comm. Partial Differential Equations, to appear (2006).

Partial regularity of weak solutions of the Navier-Stokes equations in R4 at the first blow-up time, with D. Du, Comm. Math. Phys., 273, (2007) no. 3, 785-801.

Spatial analyticity of the solutions to the sub-critical dissipative Quasi-geostrophic equations, with D. Li, Arch. Rational Mech. Anal., to appear (2006).

Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation, with D. Du, Discrete Contin. Dyn. Syst., to appear (2007).

Finite time singularities for a class of generalized surface quasi-geostrophic equations, with D. Li, Proc. Amer. Math. Soc., to appear (2007).

On the fundamental solutions for strongly parabolic systems of second order, with S. Cho and S. Kim, Indiana Univ. Math. J., to appear (2007).

Optimal local smoothing and analyticity rate estimates for the generalized Navier-Stokes equations, with D. Li, submitted (2007).

On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces, with D. Li, submitted (2007).

Higher regularity for the critical and super-critical dissipative quasi-geostrophic equations, submitted (2006).

Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains, with S. Kim, submitted (2007).

On the well-posedness for a transport equation with nonlocal velocity, submitted (2007).

A regularity criterion for the dissipative quasi-geostrophic equations, with N. Pavlovic, submitted (2007).

Finite time singularities and global well-posedness for fractal Burgers' equation, with D. Du and D. Li, submitted (2008).

A note on a certain type of traveling waves in cylinders, in preparation.

Parabolic systems with VMOx coefficients, with S. Kim and D. Kim, preprint.