Kaligirou et al (2016) recently derived a nonlocal thin-film equation model for two fluid shear flows in a channel. We discuss results on whether or not the 2+1 model equations allow smooth solutions for all time, or if there is singularity in finite time. Furthermore, we discuss existence of different branches of steady traveling wave solutions in one dimension that initially bifurcate from a flat state and present their stability and bifurcation properties, including Hopf-bifurcation to time periodic states. We also present techniques for justifying these results mathematically. We also present results on how other effects such as slip can be accommodated in this mathematical framework.