Existence and uniqueness of solutions of the Prandtl boundary layer equations

Thursday, April 30, 2015 - 2:00pm
MSB 110
Carly Sutter (Advisor: Professor Carmen Chicone)

As fluid flows past an object, it sticks to the boundary. This creates a thin layer near the boundary where fluid flow is very different than fluid flow away from the object. We call this thin layer the "boundary layer." Understanding what happens in the boundary layer plays a major role in accurately predicting drag on objects such as planes and cars. We will give an overview of how the boundary layer was discovered, and a derivation of the Prandtl boundary layer equations, which are the set of equations that describe the fluid flow in the boundary layer. While seeking a similarity solution of the Prandtl equations, we derive an ODE called the Falkner-Skan equation. If the Falkner-Skan equation paired with particular boundary conditions has a solution, then there exists a solution of the Prandtl boundary layer equations. Existence and uniqueness of the Falkner-Skan boundary value problem will be discussed in detail.