PhD in Applied Mathematics - Fluid Mechanics in Waterloo Canada | University of Waterloo

Contemporary civilization has been profoundly influenced by the enduring interplay between Mathematics and the Sciences. Within this framework, the Department of Applied Mathematics provides graduate students with specialized programs in Control Theory and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Mathematical Physics, and Scientific Computation. Student research initiatives employ advanced mathematical principles across diverse scientific disciplines, spanning from optimizing cancer treatments and manipulating shape memory alloys to processing fractal images, advancing quantum computing, and investigating climate patterns, cosmic inflation, and nanotechnology. As part of the University of Waterloo's Faculty of Mathematics - ranked 20th globally in the 2015 QS University Rankings for mathematics - our department fosters strong collaborations with the Faculties of Science and Engineering, along with numerous research centers specializing in mathematical medicine, theoretical neuroscience, quantum computing, nanotechnology, and industrial mathematics. We provide both Master's and doctoral programs, with our thesis-based Master of Mathematics (MMath) typically completed in two years. Graduates often continue to PhD studies or secure prominent roles in industry and government. The PhD program, generally completed in four years, primarily leads to academic research positions, though some graduates pursue careers in industrial, governmental, or commercial research and development.

The study of fluid dynamics involves complex nonlinear partial differential equation systems. These flows frequently operate across vastly different scales, with nonlinear interactions causing energy transfers between scales. This intricate nature has made fluid mechanics a fertile ground for mathematical innovation, continually inspiring advancements in partial differential equations, asymptotic analysis, computational techniques, and nonlinear wave phenomena - including soliton research, instability theories, chaotic systems, and stochastic modeling.