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Partial Differential Equations Research Group

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.

Faculty

  • Ning Ju

    Ph.D., Indiana, 1999. 

     

    Applied mathematics.

  • Eduardo Teixeira

    Dr. Teixeira’s research explores how structure and order emerge from nonlinear and often singular phenomena governed by partial differential equations. His work combines rigorous analysis with geometric insight, drawing on ideas from PDE theory, geometric measure theory, and applied mathematics. A central focus is the fine regularity of solutions and their interfaces—key to interpreting complex models. Ultimately, his research seeks to uncover the principles through which complexity organizes into patterns, illuminating fundamental mechanisms in mathematical and physical systems.

  • Jiahong Wu

     B.S., Peking University; Ph.D., University of Chicago, 1996.

    Nonlinear partial differential equations from fluid mechanics, geophysics, astrophysics and meteorology. Numerical linear Algebra.  He is interested in the analysis, computations and applications of these partial differential equations. One issue he has been working on is whether or not these partial differential equations are globally well-posed.

  • Xukai Yan

    B.S. University of Science and Technology of China; Ph.D. Rutgers University, 2017.

    Dr. Yan's research is on analysis of nonlinear partial differential equations and applications, recently working on equations arising from fluid dynamics and mathematical biology.

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