Fluid Film Equations and Other Applications of the Calculus of Moving Surfaces

Pavel Grinfeld
Drexel University

I will give an overview of the CMS and illustrate its capability by demonstrating a number of applications. Applications will include: 1. Boundary variation problems -- what is the change in solution of a boundary value problem induced by a change in shape? 2. Shape optimization problems -- what shape delivers an extremal value of a shape dependent objective function? 3. Dynamic problems -- I am excited to present the recently proposed exact nonlinear equations of fluid film dynamics. Derived from the Least Action Principle, these equations are a direct analogue of the Navier-Stokes equations and therefore possess the same key characteristics: conservation of mass and, in the case of inviscid equations, conservation of energy, pointwise conservation of vorticity and conservation of circulation around a closed loop.