Assistant ProfessorDepartment of MathematicsInstitute of Applied Mathematical SciencesNational Taiwan University

Office 465, Astro Math Building
No.1, Sec. 4, Roosevelt Road, Taipei, Taiwan 10617
Tel: +886 2 3366 2846
Email: vtnguyen AT ntu.edu.tw

Academic employment

Education

Research Interests: Partial Differential Equations

My research deals with the mathematical study of Nonlinear Partial Differential Equations (PDEs) arising from physics, chemistry, geometry, and biology. I have a particular interest in the study of singularity formation in Nonlinear PDEs. A singularity is formally understood as starting from a very smooth initial situation and after a time, an infinity shows up in the solution or in one of its derivatives. A fascinating aspect of studying singularities is that it describes a great variety of phenomena appearing in natural sciences and beyond. Some examples of singularities that are often crucial for their appearance in experiments or numerical simulations include reaction-diffusion equations, geometric evolution equations, nonlinear dispersive equations, free-surface flows, Euler dynamics, Bose-Einstein condensates, nonlinear wave physics, bacterial growth, black-hole cosmology, etc. Singularities often correspond to the limiting behavior of mathematical models and hence are of paramount importance in understanding their behavior. My research objective is to develop mathematical tools to analyze the formation of singularity which is one of the modern research topics relevant for the field.  Some mathematical models I have been working on

    - semilinear parabolic equations/systems;

    - geometric evolution equations: the harmonic map heat flow, and wave maps;

    - nonlinear Aggregation-Diffusion equations: the Keller-Segel system;

    - semilinear wave equations.

I also enjoy programming and doing numerical simulations of PDEs.


Selected publications (completed list: MathSciNet)

Teaching