My research interests lie in the applications of complex analysis, mainly to the following areas:
- fluid mechanics
- vortex dynamics,
- free boundary problems,
- potential theory,
- conformal mapping,
- quadrature domains and their applications.
A large element of my work has involved the theory of automorphic functions and Schottky groups.
Marshall JS, 2016, Analytical solutions for Hele-Shaw moving boundary flows in the presence of a circular cylinder, Quarterly Journal of Mechanics and Applied Mathematics, Vol:69, ISSN:0033-5614, Pages:1-33
Marshall JS, 2016, Exact solutions for Hele-Shaw free boundary flows around a flat plate of finite length, Quarterly Journal of Mechanics and Applied Mathematics, Vol:69, ISSN:0033-5614, Pages:35-66
Bromwich S, Marshall JS, 2015, Analytical solutions for annular multipolar vortex equilibria on a sphere, European Journal of Mechanics B - Fluids, Vol:53, ISSN:0997-7546, Pages:205-212