On the geophysical Green-Naghdi system (Q2073971)

The Green-Naghdi system helps model coastal oceanography because it considers the dispersive effects neglected by the shallow-water equations. The authors derive a modified Green-Naghdi system with the effect of the Coriolis force, which is a model in the equatorial oceanography to describe the propagation of large-amplitude surface waves. First, they use a semigroup approach to establish the local well-posedness of the system. Then, they investigate the effects of the Coriolis force caused by the Earth's rotation and nonlinearities on local well-posedness and traveling wave solutions. Finally, for different Coriolis parameters, they discuss the traveling wave solutions by employing the qualitative method combined with the bifurcation method of the dynamical system.