Three aspects constitute the focus of the network: The first aspect is on the derivation and validation of the governing model equations as asymptotic limit equations from the Navier–Stokes system, respectively the Euler equations. With methods from nonlinear analysis we then study different solution concepts for the respective model equations, such as existence and uniqueness of classical strong solutions and globally in time existing weak solutions. Particular attention will be turned to travelling waves as special solutions of the respective equations. The third aspect is on understanding stability and instability phenomena, depending on involved physical parameters such as gravity and surface tension. These questions will be addressed for the following fluid mechanical problems:

(A) Stability of thin-film flows on inclined planes

(B) Rimming flows

(C) Transverse (in)stabilities in water-wave model equations

Publications

Funding acknowledgement

In all project related publications, please acknowledge the funding by the DFG as follows:

"Funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — project number 545145736.“