The overarching goal of the proposed project is to study the existence and stability of front solutions for the integral boundary layer (IBL) equation and the full Navier–Stokes system as models for the dynamics of liquid flows down an inclined plane. Moreover, transversal (in)stability in two-dimensional IBL equations will be investigated.

The main steps of the project are

1.  Existence and stability of front solutions for the IBL equation

2. Existence and stability of front solutions for the Navier-Stokes system

3. Transversal stability and instability for two-dimensional IBL models