Project List for Math 497C

• Poincare-Hopf theorem (Yacov)


• Topology: Continuity of the flow map and free boundaries for objects entering the fluid domain (Elizabeth).


• Relativistic fluid dynamics (Stela).


• Differential equations, strings, and knots (Marqui).


• Kidney flow (Dustin).


• Differential equations, strings, and knots (Katrina).


• Vortex shedding in the complex plane: time-dependent Milne-Thompson theorem (Patrick)


• Pressureless Euler flows (Sharon).


• Non-radial flow in spherical coordinates: mappings to the complex plane? (Braden)


• Steady irrotational flow in particular bounded domains with N point vortices (Michael L.)


• Curl and potential flows in R^n (Mike J.)


• Poisson bracket formulation of Euler's equations in R^2: the Lax pair approach (Abe)