Vincent Martinez, PhD, is an assistant professor in the Department of Mathematics and Statistics who also serves as the applied mathematics adviser for graduate students.
His main research interests are based in the analysis of partial differential equations (PDEs), particularly those centered on hydrodynamic and geophysical equations, such as the incompressible Navier-Stokes or the quasi-geostrophic equations. He is also interested in chemotaxis equations that, for instance, incorporate the effects from the interaction of an organism with the ambient incompressible fluid, and dispersive equations with weak damping mechanisms.
A main source of inspiration in Vincent's work derives from the mathematics of turbulence, such as the identification of small length scales, and its applications, for instance, to dissipative dynamical systems or data assimilation; it continues to be a driving force in his research developments.
Vincent's work employs various tools from harmonic analysis, semigroup theory, approximation theory, control theory, as well as elliptic equations and classical energy methods.