Fangchi Yan

Dr. Yan studies partial differential equations (PDEs) that are motivated from the modeling of physical phenomena and real-world problems in general.

His research focuses on the problem of well-posedness for nonlinear dispersive equations, including the Korteweg-de Vries (KdV) equation and the nonlinear Schrödinger (NLS) equation.

His primary research interests include investigating questions of existence, uniqueness, dependence on initial data, and regularity of solutions to the initial value problem (ivp) of KdV type equations.

Also, he studies the well-posedness of the corresponding initial boundary value problem (ibvp). The study of the initial boundary value problem is based on the unified transform method, which is introduced by Fokas and his collaborators.

Dr. Yan and his collaborators have proved the well-posedness for the ibvp of KdV type equations with Dirichlet, Neumann and Robin boundary data.

Finally, Dr. Yan is also interested in the quasi-geostrophic shallow-water (QGSW) front problem.