My research is generally focused on the development and analysis of mathematical models with the aim of extracting reliable, rigorous, and useful predictions for interesting scientific problems. Such models range from deterministic and stochastic dynamical systems arising in biology, chemistry and physics, to systems of nonlinear partial differential equations such as those which (ostensibly) describe turbulent fluid flows. The techniques I use vary from the development of exact solutions, to modern approximation and asymptotic methods, careful numerical computations and simulations, to abstract functional and probabilistic analysis - often a combination of all four approaches.
Students interested in stochastic dynamics might consult recent papers including "Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes" by Yen Ting Lin, Hyejin Kim, and Charles R. Doering, Journal of Statistical Physics 148, 646-0662 (2012), while students interested in mathematical fluid dynamics are directed to my book co-authored with J. D. Gibbon, "Applied Analysis of the Navier-Stokes Equations" (Cambridge University Press Series, Graduate Texts in Applied Mathematics, 1995; corrected reprint 2005) or "The 3D Navier-Stokes Problem" by C.R. Doering, Annual Review of Fluid Mechanics Vol. 41, pp. 109-128 (2009).
