Research

My research interest lies in the field of partial differential equations. In particular, I am now working in the regularity theory of incompressible Navier-Stokes equations and compressible Navier-Stokes equations.

Publications

1.Regularity of solutions for the critical N-dimensional Burgers' equation, (with Magdalena Czubak). Preprint. pdf

2.Smoothness criteria for Navier-Stokes equations in terms of regularity along the stream lines. Submitted. pdf

3. Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations, (with Alexis Vasseur). Methods Appl. Anal. 14 (2007), no. 2, 197-212. pdf

4.The De Giorgi's Method as Applied to The Regularity Theory for Incompressible Navier Stokes Equations. Ph.D. Thesis