My research works are concerned with the mathematical analysis, numerical analysis and computational methods for the solutions of linear and nonlinear elliptic and parabolic partial differential equations focused on Fluid mechanics, Geophysics and Plasma physics. The equations include e.g. Navier-Stokes and Euler equations and their linearized ones, primitive equations and Euler-Poisson equations. I am also working on computation of the solutions for the equations with uncertainties.