Partial Differential Equations

• Hessian equations with elementary symmetric functions.

(22 pages, arXiv:math/0509487, Comm. Partial Differential Equations. 31 (2006) no. 7, 1005--1025.)

• On the Local Smoothness of Solutions of the Navier-Stokes Equations.

(joint work with Dapeng Du, 14 pages, arXiv:math/0502104, J. Math. Fluid Mech. 9 (2007), no. 2, 139--152.)

• Partial regularity of weak solutions of the Navier-Stokes equations in R^4 at the first blow up time.

(joint work with Dapeng Du, 16 pages, arXiv:math/0601113, Comm. Math. Phys., 273, (2007), no. 3, 785--801.)

• On unique continuation for the schrodinger equation with gradient vector potentials.

(joint work with Wolfgang Staubach, Proc. Amer. Math .Soc. 135 (2007), 2141-2149, arXiv:math/0603443.)

• On uniqueness of boundary blow-up solutions of a class of nonlinear elliptic equations.

(Joint work with Seick Kim and Mikhail V. Safonov, arXiv:0705.2287, accepted by Comm. Partial Differential Equations, 2006.)

• Spatial analyticity of the solutions to the sub-critical dissipative quasi-geostrophic equations.

(Joint work with Dong Li, accepted by Arch. Rational Mech. Anal., 2006.)

• Higher regularity for the critical and super-critical dissipative quasi-geostrophic equations.

(submitted, 20 pages, arXiv:math/0701826, 2006)

• On the analyticity of solutions to the Navier-Stokes equations with fractional dissipation.

(Joint work with Dong Li, 14 pages, submitted, arXiv:math/0703864, 2006.)

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

(in preparation.)

• Global well-posedness and a decay estimate for the critical quasi-geostrophic equation.

(Joint work with Dapeng Du, submitted, 9 pages, arXiv:math/0701828, 2007.)

• On the fundamental solutions for strongly parabolic systems of second order.

(Joint work with Sungwon Cho and Seick Kim, arXiv:0705.1855, submitted to IUMJ., 2007.)

• On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces.

(Joint work with Dong Li, preprint, 2007.)

• Finite time singularities for a class of generalized surface quasi-geostrophic equations.

(Joint work with Dong Li, accepted by Proc. Amer. Math .Soc., 2007.)

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

• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains.

(Joint work Seick Kim, preprint.)

Probability Theory

• About Smoothness of Solutions of the Heat Equations in Closed Smooth Space-time Domains.

(22 pages, Comm. Pure Appl. Math. 58 (2005) no. 6, 799-820, link.)

• On time inhomogeneous controlled diffusion processes in domains.

(joint work with Nicolai V. Krylov, 22 pages, Annal. Prob, 35, no. 1, 206-227, (2007), arXiv:math/0512200.)

Finite-difference Approximations

• On the Rate of Convergence of Finite-difference Approximations for Bellman's Equations with Constant Coefficients.

(joint work with Nicolai V. Krylov, Algebra i Analis (St. Petersburg Math. J.) 17 (2005), no. 2, 108-132;

translation in St. Petersburg Math. J. 17 (2006), no. 2, 295-313.)

• Rate of convergence of finite-difference approximations for degenerate linear parabolic equations with C^1 and C^2 coefficients.

(joint work with Nicolai V. Krylov, 25 pages, Electro. J. Differential Equations 2005 (2005), no. 102, 1-25, link.)

• On the rate of convergence of finite-difference approximations for bellman equations in a domain with lipschitz coefficients.

(joint work with Nicolai V. Krylov, 31 pages, Appl. Math. Optim., 56, (2007) no. 1, 37--66.)

Thesis

• On Some Problems Related to the Regularity Theory for Second-order Elliptic-Parabolic Equations and Their Numerical Approximations.

(Ph.D thesis, University of Minnesota, 2005.8, thesis advisor: Nicolai V. Krylov.)