Partial Differential Equations
The partial differential equations (PDEs) group here at OSU focuses on the analysis
and applications of several nonlinear PDEs, especially those arising in fluid mechanics,
geophysics, astrophysics, meteorology and other science and engineering practice.
The particular PDEs that the faculty members here have worked on include the Navier-Stokes
equations, the surface quasi-geostrophic equations, the Boussinesq equations, the
magnetohydrodynamics equations and other related equations. These PDEs have been at
the center of numerous analytical, experimental, and numerical investigations. One
of the most fundamental problems concerning these PDEs is whether their solutions
are globally regular or they develop singularities in a finite-time. The regularity
problem can be extremely difficult, as in the case of the 3D Navier-Stokes equations.
The global regularity problem on the 3D Navier-Stokes equations is one of the Millennium
Prize Problems. In addition, the PDEs group here is also interested in the numerical
computations and analysis of the aforementioned PDEs.