Steil, Trevor2021-01-252021-01-252020-10https://hdl.handle.net/11299/218059University of Minnesota Ph.D. dissertation. October 2020. Major: Mathematics. Advisor: Daniel Spirn. 1 computer file (PDF); 131 pages.In this work, we investigate several models of superconductivity and the motion of vortices within them. We introduce anonisothermal model that incorporates thermal fluctuations away from a critical temperature and prove global well-posedness of weak solutions in the physically relevant setting. We then prove a motion law for systems with time-dependent background potentials in terms of a simple system of ordinary differential equations. Finally, we numerically investigate the convergence of simulated vortices to these motion laws and use the motion law for time-dependent potentials to develop a heuristic for use in nonisothermal systems.enThesis or Dissertation