Fangchi Yan

Dr. Yan’s research focuses on nonlinear dispersive partial differential equations (PDEs), motivated by models in fluid dynamics, nonlinear optics, and quantum mechanics. He studies the fundamental question of well-posedness---existence, uniqueness, stability, and regularity of solutions---for both the initial value problem (ivp) and the initial-boundary value problem (ibvp).

Together with collaborators, Dr. Yan has developed a framework that combines the Fokas unified transform method with harmonic analysis in Bourgain spaces. This approach has yielded sharp results for the Korteweg--de Vries (KdV) and nonlinear Schrödinger (NLS) equations, and extends naturally to higher-order models and related systems. He also investigates ibvp in higher dimensions (including half-space and radially symmetric geometries) and works on applications to fluid mechanics, such as the quasi-geostrophic shallow-water (QGSW) front equation.