Partial Differential Equations


Group overview

This team is focused on rigorous analysis of the fundamental nonlinear differential equations occurring in scientific and engineering problems, and has natural ties with the groups in differential geometry, mathematical physics, analysis, and applied mathematics.

INFO for prospective students



Faculty Research Interests
Jingyi Chen
James Colliander Partial Differential Equations, Harmonic Analysis, Dynamical Systems
Nassif Ghoussoub Variational Methods in PDEs, Functional Inequalities, Deterministic and stochastic Optimal mass transport
Stephen Gustafson Nonlinear PDEs from applied mathematics and mathematical physics, evolution equations, stability theory, scattering.
Young-Heon Kim Optimal transport, partial differential equations, and geometry.
Sebastien Picard Differential geometry, nonlinear PDE in complex geometry, Calabi-Yau geometry
Tai-Peng Tsai Partial differential equations from mathematical physics, including fluid and dispersive PDEs
Jun-Cheng Wei Nonlinear Partial Differential Equations/Semilinear Elliptic Equations/Nonlinear,Applied and Geometric Analysis/Mathematical Biology/Singular Perturbation Problems/Phase Transition
Graduate Students Research Interests
Chen-Chih Lai Nonlinear partial differential equations, Navier–Stokes equations, Green tensor of Stokes system, complex fluid dynamics, self-similar and discretely self-similar solutions, reaction-diffusion system